Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,33,Mod(2,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 33, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.2");
S:= CuspForms(chi, 33);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 33 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.c (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.4333275711\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(15\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2.1 | ||
Character | \(\chi\) | \(=\) | 5.2 |
Dual form | 5.33.c.a.3.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −86676.0 | − | 86676.0i | −1.32257 | − | 1.32257i | −0.911689 | − | 0.410881i | \(-0.865221\pi\) |
−0.410881 | − | 0.911689i | \(-0.634779\pi\) | |||||||
\(3\) | 3.32299e7 | − | 3.32299e7i | 0.771950 | − | 0.771950i | −0.206498 | − | 0.978447i | \(-0.566207\pi\) |
0.978447 | + | 0.206498i | \(0.0662066\pi\) | |||||||
\(4\) | 1.07305e10i | 2.49838i | ||||||||
\(5\) | 1.18818e11 | + | 9.57363e10i | 0.778683 | + | 0.627418i | ||||
\(6\) | −5.76047e12 | −2.04192 | ||||||||
\(7\) | −3.06435e13 | − | 3.06435e13i | −0.922083 | − | 0.922083i | 0.0750935 | − | 0.997176i | \(-0.476074\pi\) |
−0.997176 | + | 0.0750935i | \(0.976074\pi\) | |||||||
\(8\) | 5.57804e14 | − | 5.57804e14i | 1.98172 | − | 1.98172i | ||||
\(9\) | − | 3.55432e14i | − | 0.191812i | ||||||
\(10\) | −2.00059e15 | − | 1.85967e16i | −0.200059 | − | 1.85967i | ||||
\(11\) | −5.53776e16 | −1.20518 | −0.602589 | − | 0.798052i | \(-0.705864\pi\) | ||||
−0.602589 | + | 0.798052i | \(0.705864\pi\) | |||||||
\(12\) | 3.56573e17 | + | 3.56573e17i | 1.92863 | + | 1.92863i | ||||
\(13\) | 1.61898e17 | − | 1.61898e17i | 0.243304 | − | 0.243304i | −0.574912 | − | 0.818215i | \(-0.694964\pi\) |
0.818215 | + | 0.574912i | \(0.194964\pi\) | |||||||
\(14\) | 5.31211e18i | 2.43904i | ||||||||
\(15\) | 7.12960e18 | − | 7.66989e17i | 1.08544 | − | 0.116769i | ||||
\(16\) | −5.06094e19 | −2.74354 | ||||||||
\(17\) | −2.56755e19 | − | 2.56755e19i | −0.527638 | − | 0.527638i | 0.392229 | − | 0.919868i | \(-0.371704\pi\) |
−0.919868 | + | 0.392229i | \(0.871704\pi\) | |||||||
\(18\) | −3.08074e19 | + | 3.08074e19i | −0.253685 | + | 0.253685i | ||||
\(19\) | 4.51346e20i | 1.56478i | 0.622792 | + | 0.782388i | \(0.285998\pi\) | ||||
−0.622792 | + | 0.782388i | \(0.714002\pi\) | |||||||
\(20\) | −1.02730e21 | + | 1.27497e21i | −1.56753 | + | 1.94545i | ||||
\(21\) | −2.03656e21 | −1.42360 | ||||||||
\(22\) | 4.79991e21 | + | 4.79991e21i | 1.59393 | + | 1.59393i | ||||
\(23\) | 2.16132e21 | − | 2.16132e21i | 0.352431 | − | 0.352431i | −0.508582 | − | 0.861013i | \(-0.669830\pi\) |
0.861013 | + | 0.508582i | \(0.169830\pi\) | |||||||
\(24\) | − | 3.70715e22i | − | 3.05957i | ||||||
\(25\) | 4.95218e21 | + | 2.27503e22i | 0.212694 | + | 0.977119i | ||||
\(26\) | −2.80654e22 | −0.643572 | ||||||||
\(27\) | 4.97647e22 | + | 4.97647e22i | 0.623880 | + | 0.623880i | ||||
\(28\) | 3.28820e23 | − | 3.28820e23i | 2.30372 | − | 2.30372i | ||||
\(29\) | 1.69547e23i | 0.677520i | 0.940873 | + | 0.338760i | \(0.110008\pi\) | ||||
−0.940873 | + | 0.338760i | \(0.889992\pi\) | |||||||
\(30\) | −6.84445e23 | − | 5.51486e23i | −1.59000 | − | 1.28113i | ||||
\(31\) | 6.36232e23 | 0.874638 | 0.437319 | − | 0.899306i | \(-0.355928\pi\) | ||||
0.437319 | + | 0.899306i | \(0.355928\pi\) | |||||||
\(32\) | 1.99086e24 | + | 1.99086e24i | 1.64680 | + | 1.64680i | ||||
\(33\) | −1.84019e24 | + | 1.84019e24i | −0.930337 | + | 0.930337i | ||||
\(34\) | 4.45090e24i | 1.39568i | ||||||||
\(35\) | −7.07292e23 | − | 6.57469e24i | −0.139479 | − | 1.29654i | ||||
\(36\) | 3.81395e24 | 0.479221 | ||||||||
\(37\) | 1.46477e24 | + | 1.46477e24i | 0.118725 | + | 0.118725i | 0.763973 | − | 0.645248i | \(-0.223246\pi\) |
−0.645248 | + | 0.763973i | \(0.723246\pi\) | |||||||
\(38\) | 3.91208e25 | − | 3.91208e25i | 2.06953 | − | 2.06953i | ||||
\(39\) | − | 1.07597e25i | − | 0.375636i | ||||||
\(40\) | 1.19679e26 | − | 1.28748e25i | 2.78650 | − | 0.299766i | ||||
\(41\) | −4.24771e25 | −0.666214 | −0.333107 | − | 0.942889i | \(-0.608097\pi\) | ||||
−0.333107 | + | 0.942889i | \(0.608097\pi\) | |||||||
\(42\) | 1.76521e26 | + | 1.76521e26i | 1.88282 | + | 1.88282i | ||||
\(43\) | −1.43757e26 | + | 1.43757e26i | −1.05229 | + | 1.05229i | −0.0537314 | + | 0.998555i | \(0.517111\pi\) |
−0.998555 | + | 0.0537314i | \(0.982889\pi\) | |||||||
\(44\) | − | 5.94228e26i | − | 3.01100i | ||||||
\(45\) | 3.40277e25 | − | 4.22316e25i | 0.120346 | − | 0.149361i | ||||
\(46\) | −3.74670e26 | −0.932231 | ||||||||
\(47\) | 4.39170e26 | + | 4.39170e26i | 0.774580 | + | 0.774580i | 0.978903 | − | 0.204323i | \(-0.0654993\pi\) |
−0.204323 | + | 0.978903i | \(0.565499\pi\) | |||||||
\(48\) | −1.68174e27 | + | 1.68174e27i | −2.11787 | + | 2.11787i | ||||
\(49\) | 7.73623e26i | 0.700474i | ||||||||
\(50\) | 1.54267e27 | − | 2.40114e27i | 1.01100 | − | 1.57361i | ||||
\(51\) | −1.70639e27 | −0.814621 | ||||||||
\(52\) | 1.73725e27 | + | 1.73725e27i | 0.607866 | + | 0.607866i | ||||
\(53\) | 1.94845e27 | − | 1.94845e27i | 0.502662 | − | 0.502662i | −0.409602 | − | 0.912264i | \(-0.634333\pi\) |
0.912264 | + | 0.409602i | \(0.134333\pi\) | |||||||
\(54\) | − | 8.62681e27i | − | 1.65025i | ||||||
\(55\) | −6.57984e27 | − | 5.30165e27i | −0.938452 | − | 0.756150i | ||||
\(56\) | −3.41862e28 | −3.65462 | ||||||||
\(57\) | 1.49982e28 | + | 1.49982e28i | 1.20793 | + | 1.20793i | ||||
\(58\) | 1.46957e28 | − | 1.46957e28i | 0.896068 | − | 0.896068i | ||||
\(59\) | 2.69068e28i | 1.24804i | 0.781407 | + | 0.624022i | \(0.214503\pi\) | ||||
−0.781407 | + | 0.624022i | \(0.785497\pi\) | |||||||
\(60\) | 8.23015e27 | + | 7.65041e28i | 0.291735 | + | 2.71184i | ||||
\(61\) | 1.09426e28 | 0.297744 | 0.148872 | − | 0.988856i | \(-0.452436\pi\) | ||||
0.148872 | + | 0.988856i | \(0.452436\pi\) | |||||||
\(62\) | −5.51460e28 | − | 5.51460e28i | −1.15677 | − | 1.15677i | ||||
\(63\) | −1.08917e28 | + | 1.08917e28i | −0.176867 | + | 0.176867i | ||||
\(64\) | − | 1.27755e29i | − | 1.61249i | ||||||
\(65\) | 3.47359e28 | − | 3.73682e27i | 0.342109 | − | 0.0368034i | ||||
\(66\) | 3.19001e29 | 2.46087 | ||||||||
\(67\) | 2.17368e28 | + | 2.17368e28i | 0.131825 | + | 0.131825i | 0.769941 | − | 0.638116i | \(-0.220286\pi\) |
−0.638116 | + | 0.769941i | \(0.720286\pi\) | |||||||
\(68\) | 2.75511e29 | − | 2.75511e29i | 1.31824 | − | 1.31824i | ||||
\(69\) | − | 1.43641e29i | − | 0.544119i | ||||||
\(70\) | −5.08562e29 | + | 6.31173e29i | −1.53030 | + | 1.89924i | ||||
\(71\) | 5.41700e29 | 1.29905 | 0.649524 | − | 0.760341i | \(-0.274968\pi\) | ||||
0.649524 | + | 0.760341i | \(0.274968\pi\) | |||||||
\(72\) | −1.98261e29 | − | 1.98261e29i | −0.380118 | − | 0.380118i | ||||
\(73\) | 8.08294e28 | − | 8.08294e28i | 0.124281 | − | 0.124281i | −0.642231 | − | 0.766511i | \(-0.721991\pi\) |
0.766511 | + | 0.642231i | \(0.221991\pi\) | |||||||
\(74\) | − | 2.53920e29i | − | 0.314043i | ||||||
\(75\) | 9.20551e29 | + | 5.91430e29i | 0.918476 | + | 0.590097i | ||||
\(76\) | −4.84316e30 | −3.90941 | ||||||||
\(77\) | 1.69697e30 | + | 1.69697e30i | 1.11127 | + | 1.11127i | ||||
\(78\) | −9.32610e29 | + | 9.32610e29i | −0.496805 | + | 0.496805i | ||||
\(79\) | 1.28870e30i | 0.559912i | 0.960013 | + | 0.279956i | \(0.0903199\pi\) | ||||
−0.960013 | + | 0.279956i | \(0.909680\pi\) | |||||||
\(80\) | −6.01328e30 | − | 4.84515e30i | −2.13635 | − | 1.72134i | ||||
\(81\) | 3.96597e30 | 1.15502 | ||||||||
\(82\) | 3.68175e30 | + | 3.68175e30i | 0.881114 | + | 0.881114i | ||||
\(83\) | −3.95942e30 | + | 3.95942e30i | −0.780516 | + | 0.780516i | −0.979918 | − | 0.199402i | \(-0.936100\pi\) |
0.199402 | + | 0.979918i | \(0.436100\pi\) | |||||||
\(84\) | − | 2.18533e31i | − | 3.55671i | ||||||
\(85\) | −5.92624e29 | − | 5.50878e30i | −0.0798135 | − | 0.741913i | ||||
\(86\) | 2.49206e31 | 2.78345 | ||||||||
\(87\) | 5.63403e30 | + | 5.63403e30i | 0.523012 | + | 0.523012i | ||||
\(88\) | −3.08899e31 | + | 3.08899e31i | −2.38832 | + | 2.38832i | ||||
\(89\) | 6.87798e30i | 0.443834i | 0.975066 | + | 0.221917i | \(0.0712314\pi\) | ||||
−0.975066 | + | 0.221917i | \(0.928769\pi\) | |||||||
\(90\) | −6.60985e30 | + | 7.11074e29i | −0.356707 | + | 0.0383738i | ||||
\(91\) | −9.92227e30 | −0.448692 | ||||||||
\(92\) | 2.31920e31 | + | 2.31920e31i | 0.880509 | + | 0.880509i | ||||
\(93\) | 2.11419e31 | − | 2.11419e31i | 0.675177 | − | 0.675177i | ||||
\(94\) | − | 7.61309e31i | − | 2.04887i | ||||||
\(95\) | −4.32102e31 | + | 5.36278e31i | −0.981767 | + | 1.21846i | ||||
\(96\) | 1.32312e32 | 2.54250 | ||||||||
\(97\) | −3.25578e31 | − | 3.25578e31i | −0.530039 | − | 0.530039i | 0.390545 | − | 0.920584i | \(-0.372287\pi\) |
−0.920584 | + | 0.390545i | \(0.872287\pi\) | |||||||
\(98\) | 6.70545e31 | − | 6.70545e31i | 0.926426 | − | 0.926426i | ||||
\(99\) | 1.96830e31i | 0.231168i | ||||||||
\(100\) | −2.44122e32 | + | 5.31392e31i | −2.44122 | + | 0.531392i | ||||
\(101\) | 1.95953e32 | 1.67113 | 0.835566 | − | 0.549389i | \(-0.185140\pi\) | ||||
0.835566 | + | 0.549389i | \(0.185140\pi\) | |||||||
\(102\) | 1.47903e32 | + | 1.47903e32i | 1.07739 | + | 1.07739i | ||||
\(103\) | −2.62815e31 | + | 2.62815e31i | −0.163777 | + | 0.163777i | −0.784238 | − | 0.620460i | \(-0.786946\pi\) |
0.620460 | + | 0.784238i | \(0.286946\pi\) | |||||||
\(104\) | − | 1.80615e32i | − | 0.964318i | ||||||
\(105\) | −2.41979e32 | − | 1.94973e32i | −1.10854 | − | 0.893194i | ||||
\(106\) | −3.37768e32 | −1.32961 | ||||||||
\(107\) | −3.82851e32 | − | 3.82851e32i | −1.29685 | − | 1.29685i | −0.930463 | − | 0.366385i | \(-0.880595\pi\) |
−0.366385 | − | 0.930463i | \(-0.619405\pi\) | |||||||
\(108\) | −5.33999e32 | + | 5.33999e32i | −1.55869 | + | 1.55869i | ||||
\(109\) | − | 2.58662e32i | − | 0.651491i | −0.945457 | − | 0.325746i | \(-0.894385\pi\) | ||
0.945457 | − | 0.325746i | \(-0.105615\pi\) | |||||||
\(110\) | 1.10788e32 | + | 1.02984e33i | 0.241107 | + | 2.24123i | ||||
\(111\) | 9.73480e31 | 0.183299 | ||||||||
\(112\) | 1.55085e33 | + | 1.55085e33i | 2.52977 | + | 2.52977i | ||||
\(113\) | −3.18085e32 | + | 3.18085e32i | −0.450078 | + | 0.450078i | −0.895380 | − | 0.445302i | \(-0.853096\pi\) |
0.445302 | + | 0.895380i | \(0.353096\pi\) | |||||||
\(114\) | − | 2.59996e33i | − | 3.19514i | ||||||
\(115\) | 4.63721e32 | − | 4.98861e31i | 0.495554 | − | 0.0533107i | ||||
\(116\) | −1.81932e33 | −1.69271 | ||||||||
\(117\) | −5.75438e31 | − | 5.75438e31i | −0.0466686 | − | 0.0466686i | ||||
\(118\) | 2.33217e33 | − | 2.33217e33i | 1.65063 | − | 1.65063i | ||||
\(119\) | 1.57358e33i | 0.973053i | ||||||||
\(120\) | 3.54909e33 | − | 4.40475e33i | 1.91963 | − | 2.38244i | ||||
\(121\) | 9.55303e32 | 0.452455 | ||||||||
\(122\) | −9.48460e32 | − | 9.48460e32i | −0.393788 | − | 0.393788i | ||||
\(123\) | −1.41151e33 | + | 1.41151e33i | −0.514283 | + | 0.514283i | ||||
\(124\) | 6.82707e33i | 2.18518i | ||||||||
\(125\) | −1.58963e33 | + | 3.17724e33i | −0.447440 | + | 0.894314i | ||||
\(126\) | 1.88809e33 | 0.467837 | ||||||||
\(127\) | −2.69610e32 | − | 2.69610e32i | −0.0588676 | − | 0.0588676i | 0.677060 | − | 0.735928i | \(-0.263254\pi\) |
−0.735928 | + | 0.677060i | \(0.763254\pi\) | |||||||
\(128\) | −2.52256e33 | + | 2.52256e33i | −0.485828 | + | 0.485828i | ||||
\(129\) | 9.55407e33i | 1.62462i | ||||||||
\(130\) | −3.33466e33 | − | 2.68688e33i | −0.501139 | − | 0.403789i | ||||
\(131\) | 5.95457e33 | 0.791607 | 0.395803 | − | 0.918335i | \(-0.370466\pi\) | ||||
0.395803 | + | 0.918335i | \(0.370466\pi\) | |||||||
\(132\) | −1.97461e34 | − | 1.97461e34i | −2.32434 | − | 2.32434i | ||||
\(133\) | 1.38308e34 | − | 1.38308e34i | 1.44285 | − | 1.44285i | ||||
\(134\) | − | 3.76811e33i | − | 0.348696i | ||||||
\(135\) | 1.14863e33 | + | 1.06772e34i | 0.0943715 | + | 0.877238i | ||||
\(136\) | −2.86438e34 | −2.09126 | ||||||||
\(137\) | −1.77917e33 | − | 1.77917e33i | −0.115528 | − | 0.115528i | 0.646979 | − | 0.762507i | \(-0.276032\pi\) |
−0.762507 | + | 0.646979i | \(0.776032\pi\) | |||||||
\(138\) | −1.24502e34 | + | 1.24502e34i | −0.719635 | + | 0.719635i | ||||
\(139\) | 2.18631e34i | 1.12584i | 0.826513 | + | 0.562918i | \(0.190321\pi\) | ||||
−0.826513 | + | 0.562918i | \(0.809679\pi\) | |||||||
\(140\) | 7.05495e34 | − | 7.58958e33i | 3.23926 | − | 0.348473i | ||||
\(141\) | 2.91871e34 | 1.19587 | ||||||||
\(142\) | −4.69523e34 | − | 4.69523e34i | −1.71808 | − | 1.71808i | ||||
\(143\) | −8.96554e33 | + | 8.96554e33i | −0.293224 | + | 0.293224i | ||||
\(144\) | 1.79882e34i | 0.526244i | ||||||||
\(145\) | −1.62318e34 | + | 2.01452e34i | −0.425088 | + | 0.527574i | ||||
\(146\) | −1.40119e34 | −0.328740 | ||||||||
\(147\) | 2.57074e34 | + | 2.57074e34i | 0.540731 | + | 0.540731i | ||||
\(148\) | −1.57176e34 | + | 1.57176e34i | −0.296619 | + | 0.296619i | ||||
\(149\) | 1.48607e34i | 0.251802i | 0.992043 | + | 0.125901i | \(0.0401822\pi\) | ||||
−0.992043 | + | 0.125901i | \(0.959818\pi\) | |||||||
\(150\) | −2.85269e34 | − | 1.31052e35i | −0.434304 | − | 1.99519i | ||||
\(151\) | −8.95001e34 | −1.22516 | −0.612580 | − | 0.790409i | \(-0.709868\pi\) | ||||
−0.612580 | + | 0.790409i | \(0.709868\pi\) | |||||||
\(152\) | 2.51763e35 | + | 2.51763e35i | 3.10094 | + | 3.10094i | ||||
\(153\) | −9.12590e33 | + | 9.12590e33i | −0.101208 | + | 0.101208i | ||||
\(154\) | − | 2.94172e35i | − | 2.93948i | ||||||
\(155\) | 7.55956e34 | + | 6.09105e34i | 0.681066 | + | 0.548763i | ||||
\(156\) | 1.15457e35 | 0.938484 | ||||||||
\(157\) | −7.21862e34 | − | 7.21862e34i | −0.529736 | − | 0.529736i | 0.390758 | − | 0.920494i | \(-0.372213\pi\) |
−0.920494 | + | 0.390758i | \(0.872213\pi\) | |||||||
\(158\) | 1.11700e35 | − | 1.11700e35i | 0.740523 | − | 0.740523i | ||||
\(159\) | − | 1.29494e35i | − | 0.776059i | ||||||
\(160\) | 4.59517e34 | + | 4.27148e35i | 0.249105 | + | 2.31557i | ||||
\(161\) | −1.32461e35 | −0.649942 | ||||||||
\(162\) | −3.43755e35 | − | 3.43755e35i | −1.52760 | − | 1.52760i | ||||
\(163\) | −1.69172e35 | + | 1.69172e35i | −0.681281 | + | 0.681281i | −0.960289 | − | 0.279008i | \(-0.909994\pi\) |
0.279008 | + | 0.960289i | \(0.409994\pi\) | |||||||
\(164\) | − | 4.55800e35i | − | 1.66446i | ||||||
\(165\) | −3.94821e35 | + | 4.24740e34i | −1.30815 | + | 0.140728i | ||||
\(166\) | 6.86373e35 | 2.06457 | ||||||||
\(167\) | 4.19852e35 | + | 4.19852e35i | 1.14718 | + | 1.14718i | 0.987104 | + | 0.160079i | \(0.0511748\pi\) |
0.160079 | + | 0.987104i | \(0.448825\pi\) | |||||||
\(168\) | −1.13600e36 | + | 1.13600e36i | −2.82118 | + | 2.82118i | ||||
\(169\) | 3.90357e35i | 0.881607i | ||||||||
\(170\) | −4.26113e35 | + | 5.28845e35i | −0.875673 | + | 1.08679i | ||||
\(171\) | 1.60423e35 | 0.300143 | ||||||||
\(172\) | −1.54258e36 | − | 1.54258e36i | −2.62902 | − | 2.62902i | ||||
\(173\) | 5.15326e34 | − | 5.15326e34i | 0.0800469 | − | 0.0800469i | −0.665950 | − | 0.745997i | \(-0.731973\pi\) |
0.745997 | + | 0.665950i | \(0.231973\pi\) | |||||||
\(174\) | − | 9.76670e35i | − | 1.38344i | ||||||
\(175\) | 5.45398e35 | − | 8.48902e35i | 0.704863 | − | 1.09711i | ||||
\(176\) | 2.80263e36 | 3.30645 | ||||||||
\(177\) | 8.94111e35 | + | 8.94111e35i | 0.963427 | + | 0.963427i | ||||
\(178\) | 5.96155e35 | − | 5.96155e35i | 0.587002 | − | 0.587002i | ||||
\(179\) | 3.86229e35i | 0.347694i | 0.984773 | + | 0.173847i | \(0.0556197\pi\) | ||||
−0.984773 | + | 0.173847i | \(0.944380\pi\) | |||||||
\(180\) | 4.53165e35 | + | 3.65134e35i | 0.373161 | + | 0.300671i | ||||
\(181\) | −8.84555e35 | −0.666603 | −0.333302 | − | 0.942820i | \(-0.608163\pi\) | ||||
−0.333302 | + | 0.942820i | \(0.608163\pi\) | |||||||
\(182\) | 8.60022e35 | + | 8.60022e35i | 0.593427 | + | 0.593427i | ||||
\(183\) | 3.63622e35 | − | 3.63622e35i | 0.229843 | − | 0.229843i | ||||
\(184\) | − | 2.41119e36i | − | 1.39684i | ||||||
\(185\) | 3.38087e34 | + | 3.14271e35i | 0.0179589 | + | 0.166939i | ||||
\(186\) | −3.66499e36 | −1.78594 | ||||||||
\(187\) | 1.42185e36 | + | 1.42185e36i | 0.635898 | + | 0.635898i | ||||
\(188\) | −4.71250e36 | + | 4.71250e36i | −1.93520 | + | 1.93520i | ||||
\(189\) | − | 3.04993e36i | − | 1.15054i | ||||||
\(190\) | 8.39353e36 | − | 9.02959e35i | 2.90996 | − | 0.313048i | ||||
\(191\) | 3.61819e36 | 1.15334 | 0.576670 | − | 0.816977i | \(-0.304352\pi\) | ||||
0.576670 | + | 0.816977i | \(0.304352\pi\) | |||||||
\(192\) | −4.24528e36 | − | 4.24528e36i | −1.24476 | − | 1.24476i | ||||
\(193\) | −3.74741e36 | + | 3.74741e36i | −1.01115 | + | 1.01115i | −0.0112097 | + | 0.999937i | \(0.503568\pi\) |
−0.999937 | + | 0.0112097i | \(0.996432\pi\) | |||||||
\(194\) | 5.64397e36i | 1.40203i | ||||||||
\(195\) | 1.03010e36 | − | 1.27844e36i | 0.235681 | − | 0.292502i | ||||
\(196\) | −8.30134e36 | −1.75005 | ||||||||
\(197\) | −4.47450e36 | − | 4.47450e36i | −0.869531 | − | 0.869531i | 0.122890 | − | 0.992420i | \(-0.460784\pi\) |
−0.992420 | + | 0.122890i | \(0.960784\pi\) | |||||||
\(198\) | 1.70604e36 | − | 1.70604e36i | 0.305736 | − | 0.305736i | ||||
\(199\) | 1.12924e37i | 1.86697i | 0.358610 | + | 0.933487i | \(0.383251\pi\) | ||||
−0.358610 | + | 0.933487i | \(0.616749\pi\) | |||||||
\(200\) | 1.54526e37 | + | 9.92788e36i | 2.35787 | + | 1.51487i | ||||
\(201\) | 1.44462e36 | 0.203525 | ||||||||
\(202\) | −1.69845e37 | − | 1.69845e37i | −2.21019 | − | 2.21019i | ||||
\(203\) | 5.19552e36 | − | 5.19552e36i | 0.624730 | − | 0.624730i | ||||
\(204\) | − | 1.83104e37i | − | 2.03523i | ||||||
\(205\) | −5.04703e36 | − | 4.06660e36i | −0.518769 | − | 0.417994i | ||||
\(206\) | 4.55594e36 | 0.433214 | ||||||||
\(207\) | −7.68204e35 | − | 7.68204e35i | −0.0676006 | − | 0.0676006i | ||||
\(208\) | −8.19357e36 | + | 8.19357e36i | −0.667513 | + | 0.667513i | ||||
\(209\) | − | 2.49945e37i | − | 1.88583i | ||||||
\(210\) | 4.07433e36 | + | 3.78733e37i | 0.284805 | + | 2.64743i | ||||
\(211\) | −1.68200e37 | −1.08970 | −0.544849 | − | 0.838534i | \(-0.683413\pi\) | ||||
−0.544849 | + | 0.838534i | \(0.683413\pi\) | |||||||
\(212\) | 2.09078e37 | + | 2.09078e37i | 1.25584 | + | 1.25584i | ||||
\(213\) | 1.80006e37 | − | 1.80006e37i | 1.00280 | − | 1.00280i | ||||
\(214\) | 6.63679e37i | 3.43035i | ||||||||
\(215\) | −3.08437e37 | + | 3.31810e36i | −1.47962 | + | 0.159175i | ||||
\(216\) | 5.55179e37 | 2.47271 | ||||||||
\(217\) | −1.94964e37 | − | 1.94964e37i | −0.806489 | − | 0.806489i | ||||
\(218\) | −2.24198e37 | + | 2.24198e37i | −0.861643 | + | 0.861643i | ||||
\(219\) | − | 5.37190e36i | − | 0.191877i | ||||||
\(220\) | 5.68892e37 | − | 7.06048e37i | 1.88915 | − | 2.34461i | ||||
\(221\) | −8.31364e36 | −0.256753 | ||||||||
\(222\) | −8.43773e36 | − | 8.43773e36i | −0.242425 | − | 0.242425i | ||||
\(223\) | 1.11820e37 | − | 1.11820e37i | 0.298980 | − | 0.298980i | −0.541634 | − | 0.840614i | \(-0.682194\pi\) |
0.840614 | + | 0.541634i | \(0.182194\pi\) | |||||||
\(224\) | − | 1.22014e38i | − | 3.03698i | ||||||
\(225\) | 8.08619e36 | − | 1.76016e36i | 0.187423 | − | 0.0407974i | ||||
\(226\) | 5.51406e37 | 1.19052 | ||||||||
\(227\) | 1.90311e37 | + | 1.90311e37i | 0.382870 | + | 0.382870i | 0.872135 | − | 0.489265i | \(-0.162735\pi\) |
−0.489265 | + | 0.872135i | \(0.662735\pi\) | |||||||
\(228\) | −1.60938e38 | + | 1.60938e38i | −3.01787 | + | 3.01787i | ||||
\(229\) | − | 6.59696e37i | − | 1.15339i | −0.816960 | − | 0.576695i | \(-0.804342\pi\) | ||
0.816960 | − | 0.576695i | \(-0.195658\pi\) | |||||||
\(230\) | −4.45174e37 | − | 3.58695e37i | −0.725912 | − | 0.584898i | ||||
\(231\) | 1.12780e38 | 1.71570 | ||||||||
\(232\) | 9.45741e37 | + | 9.45741e37i | 1.34265 | + | 1.34265i | ||||
\(233\) | −4.83253e37 | + | 4.83253e37i | −0.640442 | + | 0.640442i | −0.950664 | − | 0.310222i | \(-0.899597\pi\) |
0.310222 | + | 0.950664i | \(0.399597\pi\) | |||||||
\(234\) | 9.97533e36i | 0.123445i | ||||||||
\(235\) | 1.01366e37 | + | 9.42255e37i | 0.117167 | + | 1.08914i | ||||
\(236\) | −2.88723e38 | −3.11809 | ||||||||
\(237\) | 4.28235e37 | + | 4.28235e37i | 0.432224 | + | 0.432224i | ||||
\(238\) | 1.36391e38 | − | 1.36391e38i | 1.28693 | − | 1.28693i | ||||
\(239\) | − | 9.02438e37i | − | 0.796253i | −0.917331 | − | 0.398127i | \(-0.869661\pi\) | ||
0.917331 | − | 0.398127i | \(-0.130339\pi\) | |||||||
\(240\) | −3.60825e38 | + | 3.88168e37i | −2.97794 | + | 0.320361i | ||||
\(241\) | −5.86486e37 | −0.452882 | −0.226441 | − | 0.974025i | \(-0.572709\pi\) | ||||
−0.226441 | + | 0.974025i | \(0.572709\pi\) | |||||||
\(242\) | −8.28018e37 | − | 8.28018e37i | −0.598403 | − | 0.598403i | ||||
\(243\) | 3.95739e37 | − | 3.95739e37i | 0.267737 | − | 0.267737i | ||||
\(244\) | 1.17419e38i | 0.743879i | ||||||||
\(245\) | −7.40638e37 | + | 9.19200e37i | −0.439490 | + | 0.545447i | ||||
\(246\) | 2.44688e38 | 1.36035 | ||||||||
\(247\) | 7.30721e37 | + | 7.30721e37i | 0.380715 | + | 0.380715i | ||||
\(248\) | 3.54893e38 | − | 3.54893e38i | 1.73329 | − | 1.73329i | ||||
\(249\) | 2.63142e38i | 1.20504i | ||||||||
\(250\) | 4.13173e38 | − | 1.37608e38i | 1.77456 | − | 0.591022i | ||||
\(251\) | 2.01611e38 | 0.812335 | 0.406168 | − | 0.913799i | \(-0.366865\pi\) | ||||
0.406168 | + | 0.913799i | \(0.366865\pi\) | |||||||
\(252\) | −1.16873e38 | − | 1.16873e38i | −0.441881 | − | 0.441881i | ||||
\(253\) | −1.19689e38 | + | 1.19689e38i | −0.424743 | + | 0.424743i | ||||
\(254\) | 4.67374e37i | 0.155713i | ||||||||
\(255\) | −2.02749e38 | − | 1.63363e38i | −0.634331 | − | 0.511107i | ||||
\(256\) | −1.11411e38 | −0.327408 | ||||||||
\(257\) | 1.06669e38 | + | 1.06669e38i | 0.294514 | + | 0.294514i | 0.838861 | − | 0.544346i | \(-0.183222\pi\) |
−0.544346 | + | 0.838861i | \(0.683222\pi\) | |||||||
\(258\) | 8.28108e38 | − | 8.28108e38i | 2.14868 | − | 2.14868i | ||||
\(259\) | − | 8.97711e37i | − | 0.218948i | ||||||
\(260\) | 4.00979e37 | + | 3.72733e38i | 0.0919491 | + | 0.854721i | ||||
\(261\) | 6.02624e37 | 0.129957 | ||||||||
\(262\) | −5.16118e38 | − | 5.16118e38i | −1.04696 | − | 1.04696i | ||||
\(263\) | −3.24189e38 | + | 3.24189e38i | −0.618737 | + | 0.618737i | −0.945207 | − | 0.326470i | \(-0.894141\pi\) |
0.326470 | + | 0.945207i | \(0.394141\pi\) | |||||||
\(264\) | 2.05293e39i | 3.68733i | ||||||||
\(265\) | 4.18048e38 | − | 4.49728e37i | 0.706793 | − | 0.0760354i | ||||
\(266\) | −2.39760e39 | −3.81655 | ||||||||
\(267\) | 2.28555e38 | + | 2.28555e38i | 0.342618 | + | 0.342618i | ||||
\(268\) | −2.33246e38 | + | 2.33246e38i | −0.329350 | + | 0.329350i | ||||
\(269\) | − | 9.40374e38i | − | 1.25102i | −0.780217 | − | 0.625510i | \(-0.784891\pi\) | ||
0.780217 | − | 0.625510i | \(-0.215109\pi\) | |||||||
\(270\) | 8.25899e38 | − | 1.02502e39i | 1.03540 | − | 1.28502i | ||||
\(271\) | −1.17019e39 | −1.38277 | −0.691384 | − | 0.722487i | \(-0.742999\pi\) | ||||
−0.691384 | + | 0.722487i | \(0.742999\pi\) | |||||||
\(272\) | 1.29942e39 | + | 1.29942e39i | 1.44760 | + | 1.44760i | ||||
\(273\) | −3.29716e38 | + | 3.29716e38i | −0.346368 | + | 0.346368i | ||||
\(274\) | 3.08422e38i | 0.305588i | ||||||||
\(275\) | −2.74240e38 | − | 1.25986e39i | −0.256335 | − | 1.17760i | ||||
\(276\) | 1.54134e39 | 1.35942 | ||||||||
\(277\) | 5.47028e38 | + | 5.47028e38i | 0.455338 | + | 0.455338i | 0.897122 | − | 0.441784i | \(-0.145654\pi\) |
−0.441784 | + | 0.897122i | \(0.645654\pi\) | |||||||
\(278\) | 1.89501e39 | − | 1.89501e39i | 1.48900 | − | 1.48900i | ||||
\(279\) | − | 2.26137e38i | − | 0.167766i | ||||||
\(280\) | −4.06192e39 | − | 3.27286e39i | −2.84579 | − | 2.29297i | ||||
\(281\) | 8.75207e38 | 0.579175 | 0.289587 | − | 0.957152i | \(-0.406482\pi\) | ||||
0.289587 | + | 0.957152i | \(0.406482\pi\) | |||||||
\(282\) | −2.52982e39 | − | 2.52982e39i | −1.58163 | − | 1.58163i | ||||
\(283\) | −7.09866e38 | + | 7.09866e38i | −0.419366 | + | 0.419366i | −0.884985 | − | 0.465619i | \(-0.845832\pi\) |
0.465619 | + | 0.884985i | \(0.345832\pi\) | |||||||
\(284\) | 5.81270e39i | 3.24552i | ||||||||
\(285\) | 3.46177e38 | + | 3.21792e39i | 0.182718 | + | 1.69847i | ||||
\(286\) | 1.55419e39 | 0.775619 | ||||||||
\(287\) | 1.30165e39 | + | 1.30165e39i | 0.614304 | + | 0.614304i | ||||
\(288\) | 7.07617e38 | − | 7.07617e38i | 0.315877 | − | 0.315877i | ||||
\(289\) | − | 1.04945e39i | − | 0.443195i | ||||||
\(290\) | 3.15301e39 | − | 3.39195e38i | 1.25996 | − | 0.135544i | ||||
\(291\) | −2.16379e39 | −0.818327 | ||||||||
\(292\) | 8.67338e38 | + | 8.67338e38i | 0.310501 | + | 0.310501i | ||||
\(293\) | 1.23887e38 | − | 1.23887e38i | 0.0419897 | − | 0.0419897i | −0.685800 | − | 0.727790i | \(-0.740548\pi\) |
0.727790 | + | 0.685800i | \(0.240548\pi\) | |||||||
\(294\) | − | 4.45643e39i | − | 1.43031i | ||||||
\(295\) | −2.57596e39 | + | 3.19700e39i | −0.783045 | + | 0.971831i | ||||
\(296\) | 1.63410e39 | 0.470557 | ||||||||
\(297\) | −2.75585e39 | − | 2.75585e39i | −0.751887 | − | 0.751887i | ||||
\(298\) | 1.28807e39 | − | 1.28807e39i | 0.333026 | − | 0.333026i | ||||
\(299\) | − | 6.99829e38i | − | 0.171496i | ||||||
\(300\) | −6.34633e39 | + | 9.87795e39i | −1.47429 | + | 2.29471i | ||||
\(301\) | 8.81045e39 | 1.94059 | ||||||||
\(302\) | 7.75751e39 | + | 7.75751e39i | 1.62036 | + | 1.62036i | ||||
\(303\) | 6.51151e39 | − | 6.51151e39i | 1.29003 | − | 1.29003i | ||||
\(304\) | − | 2.28423e40i | − | 4.29302i | ||||||
\(305\) | 1.30017e39 | + | 1.04760e39i | 0.231848 | + | 0.186810i | ||||
\(306\) | 1.58199e39 | 0.267708 | ||||||||
\(307\) | 1.44230e38 | + | 1.44230e38i | 0.0231655 | + | 0.0231655i | 0.718595 | − | 0.695429i | \(-0.244786\pi\) |
−0.695429 | + | 0.718595i | \(0.744786\pi\) | |||||||
\(308\) | −1.82092e40 | + | 1.82092e40i | −2.77639 | + | 2.77639i | ||||
\(309\) | 1.74666e39i | 0.252856i | ||||||||
\(310\) | −1.27284e39 | − | 1.18318e40i | −0.174979 | − | 1.62654i | ||||
\(311\) | −3.54229e39 | −0.462507 | −0.231253 | − | 0.972894i | \(-0.574283\pi\) | ||||
−0.231253 | + | 0.972894i | \(0.574283\pi\) | |||||||
\(312\) | −6.00182e39 | − | 6.00182e39i | −0.744405 | − | 0.744405i | ||||
\(313\) | 2.68158e39 | − | 2.68158e39i | 0.315995 | − | 0.315995i | −0.531231 | − | 0.847227i | \(-0.678271\pi\) |
0.847227 | + | 0.531231i | \(0.178271\pi\) | |||||||
\(314\) | 1.25136e40i | 1.40123i | ||||||||
\(315\) | −2.33685e39 | + | 2.51394e38i | −0.248692 | + | 0.0267538i | ||||
\(316\) | −1.38284e40 | −1.39888 | ||||||||
\(317\) | 5.96351e39 | + | 5.96351e39i | 0.573527 | + | 0.573527i | 0.933112 | − | 0.359585i | \(-0.117082\pi\) |
−0.359585 | + | 0.933112i | \(0.617082\pi\) | |||||||
\(318\) | −1.12240e40 | + | 1.12240e40i | −1.02639 | + | 1.02639i | ||||
\(319\) | − | 9.38911e39i | − | 0.816533i | ||||||
\(320\) | 1.22308e40 | − | 1.51795e40i | 1.01171 | − | 1.25562i | ||||
\(321\) | −2.54442e40 | −2.00220 | ||||||||
\(322\) | 1.14812e40 | + | 1.14812e40i | 0.859594 | + | 0.859594i | ||||
\(323\) | 1.15885e40 | − | 1.15885e40i | 0.825636 | − | 0.825636i | ||||
\(324\) | 4.25568e40i | 2.88568i | ||||||||
\(325\) | 4.48499e39 | + | 2.88149e39i | 0.289486 | + | 0.185987i | ||||
\(326\) | 2.93263e40 | 1.80208 | ||||||||
\(327\) | −8.59531e39 | − | 8.59531e39i | −0.502918 | − | 0.502918i | ||||
\(328\) | −2.36939e40 | + | 2.36939e40i | −1.32025 | + | 1.32025i | ||||
\(329\) | − | 2.69154e40i | − | 1.42845i | ||||||
\(330\) | 3.79029e40 | + | 3.05400e40i | 1.91624 | + | 1.54399i | ||||
\(331\) | −1.21325e40 | −0.584388 | −0.292194 | − | 0.956359i | \(-0.594385\pi\) | ||||
−0.292194 | + | 0.956359i | \(0.594385\pi\) | |||||||
\(332\) | −4.24864e40 | − | 4.24864e40i | −1.95003 | − | 1.95003i | ||||
\(333\) | 5.20624e38 | − | 5.20624e38i | 0.0227728 | − | 0.0227728i | ||||
\(334\) | − | 7.27822e40i | − | 3.03446i | ||||||
\(335\) | 5.01712e38 | + | 4.66371e39i | 0.0199406 | + | 0.185359i | ||||
\(336\) | 1.03069e41 | 3.90571 | ||||||||
\(337\) | −2.74022e40 | − | 2.74022e40i | −0.990165 | − | 0.990165i | 0.00978662 | − | 0.999952i | \(-0.496885\pi\) |
−0.999952 | + | 0.00978662i | \(0.996885\pi\) | |||||||
\(338\) | 3.38346e40 | − | 3.38346e40i | 1.16599 | − | 1.16599i | ||||
\(339\) | 2.11399e40i | 0.694875i | ||||||||
\(340\) | 5.91119e40 | − | 6.35914e39i | 1.85358 | − | 0.199405i | ||||
\(341\) | −3.52330e40 | −1.05410 | ||||||||
\(342\) | −1.39048e40 | − | 1.39048e40i | −0.396960 | − | 0.396960i | ||||
\(343\) | −1.01370e40 | + | 1.01370e40i | −0.276188 | + | 0.276188i | ||||
\(344\) | 1.60377e41i | 4.17067i | ||||||||
\(345\) | 1.37517e40 | − | 1.70671e40i | 0.341389 | − | 0.423696i | ||||
\(346\) | −8.93327e39 | −0.211735 | ||||||||
\(347\) | 3.03445e40 | + | 3.03445e40i | 0.686766 | + | 0.686766i | 0.961516 | − | 0.274750i | \(-0.0885950\pi\) |
−0.274750 | + | 0.961516i | \(0.588595\pi\) | |||||||
\(348\) | −6.04559e40 | + | 6.04559e40i | −1.30668 | + | 1.30668i | ||||
\(349\) | 6.34527e40i | 1.30992i | 0.755665 | + | 0.654958i | \(0.227314\pi\) | ||||
−0.755665 | + | 0.654958i | \(0.772686\pi\) | |||||||
\(350\) | −1.20852e41 | + | 2.63065e40i | −2.38323 | + | 0.518770i | ||||
\(351\) | 1.61136e40 | 0.303585 | ||||||||
\(352\) | −1.10249e41 | − | 1.10249e41i | −1.98469 | − | 1.98469i | ||||
\(353\) | 2.28151e40 | − | 2.28151e40i | 0.392489 | − | 0.392489i | −0.483085 | − | 0.875574i | \(-0.660484\pi\) |
0.875574 | + | 0.483085i | \(0.160484\pi\) | |||||||
\(354\) | − | 1.54996e41i | − | 2.54840i | ||||||
\(355\) | 6.43635e40 | + | 5.18603e40i | 1.01155 | + | 0.815045i | ||||
\(356\) | −7.38040e40 | −1.10887 | ||||||||
\(357\) | 5.22898e40 | + | 5.22898e40i | 0.751148 | + | 0.751148i | ||||
\(358\) | 3.34768e40 | − | 3.34768e40i | 0.459849 | − | 0.459849i | ||||
\(359\) | − | 6.43148e40i | − | 0.844889i | −0.906389 | − | 0.422445i | \(-0.861172\pi\) | ||
0.906389 | − | 0.422445i | \(-0.138828\pi\) | |||||||
\(360\) | −4.57613e39 | − | 4.25378e40i | −0.0574987 | − | 0.534484i | ||||
\(361\) | −1.20515e41 | −1.44852 | ||||||||
\(362\) | 7.66696e40 | + | 7.66696e40i | 0.881630 | + | 0.881630i | ||||
\(363\) | 3.17446e40 | − | 3.17446e40i | 0.349272 | − | 0.349272i | ||||
\(364\) | − | 1.06471e41i | − | 1.12101i | ||||||
\(365\) | 1.73423e40 | − | 1.86564e39i | 0.174751 | − | 0.0187994i | ||||
\(366\) | −6.30345e40 | −0.607968 | ||||||||
\(367\) | 1.05697e41 | + | 1.05697e41i | 0.975904 | + | 0.975904i | 0.999716 | − | 0.0238129i | \(-0.00758060\pi\) |
−0.0238129 | + | 0.999716i | \(0.507581\pi\) | |||||||
\(368\) | −1.09383e41 | + | 1.09383e41i | −0.966909 | + | 0.966909i | ||||
\(369\) | 1.50977e40i | 0.127788i | ||||||||
\(370\) | 2.43094e40 | − | 3.01701e40i | 0.197036 | − | 0.244540i | ||||
\(371\) | −1.19415e41 | −0.926991 | ||||||||
\(372\) | 2.26863e41 | + | 2.26863e41i | 1.68685 | + | 1.68685i | ||||
\(373\) | 1.48816e41 | − | 1.48816e41i | 1.06001 | − | 1.06001i | 0.0619275 | − | 0.998081i | \(-0.480275\pi\) |
0.998081 | − | 0.0619275i | \(-0.0197248\pi\) | |||||||
\(374\) | − | 2.46480e41i | − | 1.68204i | ||||||
\(375\) | 5.27563e40 | + | 1.58403e41i | 0.344964 | + | 1.03577i | ||||
\(376\) | 4.89941e41 | 3.07000 | ||||||||
\(377\) | 2.74494e40 | + | 2.74494e40i | 0.164843 | + | 0.164843i | ||||
\(378\) | −2.64356e41 | + | 2.64356e41i | −1.52167 | + | 1.52167i | ||||
\(379\) | − | 5.82696e40i | − | 0.321525i | −0.986993 | − | 0.160762i | \(-0.948605\pi\) | ||
0.986993 | − | 0.160762i | \(-0.0513953\pi\) | |||||||
\(380\) | −5.75452e41 | − | 4.63666e41i | −3.04419 | − | 2.45283i | ||||
\(381\) | −1.79182e40 | −0.0908856 | ||||||||
\(382\) | −3.13610e41 | − | 3.13610e41i | −1.52537 | − | 1.52537i | ||||
\(383\) | −1.79346e41 | + | 1.79346e41i | −0.836587 | + | 0.836587i | −0.988408 | − | 0.151821i | \(-0.951486\pi\) |
0.151821 | + | 0.988408i | \(0.451486\pi\) | |||||||
\(384\) | 1.67649e41i | 0.750069i | ||||||||
\(385\) | 3.91681e40 | + | 3.64091e41i | 0.168097 | + | 1.56256i | ||||
\(386\) | 6.49621e41 | 2.67463 | ||||||||
\(387\) | 5.10959e40 | + | 5.10959e40i | 0.201841 | + | 0.201841i | ||||
\(388\) | 3.49361e41 | − | 3.49361e41i | 1.32424 | − | 1.32424i | ||||
\(389\) | 1.82784e41i | 0.664882i | 0.943124 | + | 0.332441i | \(0.107872\pi\) | ||||
−0.943124 | + | 0.332441i | \(0.892128\pi\) | |||||||
\(390\) | −2.00095e41 | + | 2.15258e40i | −0.698558 | + | 0.0751495i | ||||
\(391\) | −1.10986e41 | −0.371913 | ||||||||
\(392\) | 4.31530e41 | + | 4.31530e41i | 1.38814 | + | 1.38814i | ||||
\(393\) | 1.97870e41 | − | 1.97870e41i | 0.611081 | − | 0.611081i | ||||
\(394\) | 7.75663e41i | 2.30003i | ||||||||
\(395\) | −1.23376e41 | + | 1.53121e41i | −0.351299 | + | 0.435994i | ||||
\(396\) | −2.11208e41 | −0.577546 | ||||||||
\(397\) | −4.90080e41 | − | 4.90080e41i | −1.28712 | − | 1.28712i | −0.936528 | − | 0.350592i | \(-0.885980\pi\) |
−0.350592 | − | 0.936528i | \(-0.614020\pi\) | |||||||
\(398\) | 9.78783e41 | − | 9.78783e41i | 2.46921 | − | 2.46921i | ||||
\(399\) | − | 9.19194e41i | − | 2.22762i | ||||||
\(400\) | −2.50627e41 | − | 1.15138e42i | −0.583536 | − | 2.68076i | ||||
\(401\) | −8.88117e41 | −1.98683 | −0.993413 | − | 0.114586i | \(-0.963446\pi\) | ||||
−0.993413 | + | 0.114586i | \(0.963446\pi\) | |||||||
\(402\) | −1.25214e41 | − | 1.25214e41i | −0.269176 | − | 0.269176i | ||||
\(403\) | 1.03005e41 | − | 1.03005e41i | 0.212803 | − | 0.212803i | ||||
\(404\) | 2.10267e42i | 4.17513i | ||||||||
\(405\) | 4.71228e41 | + | 3.79688e41i | 0.899395 | + | 0.724680i | ||||
\(406\) | −9.00653e41 | −1.65250 | ||||||||
\(407\) | −8.11152e40 | − | 8.11152e40i | −0.143084 | − | 0.143084i | ||||
\(408\) | −9.51831e41 | + | 9.51831e41i | −1.61435 | + | 1.61435i | ||||
\(409\) | − | 3.63748e41i | − | 0.593236i | −0.954996 | − | 0.296618i | \(-0.904141\pi\) | ||
0.954996 | − | 0.296618i | \(-0.0958588\pi\) | |||||||
\(410\) | 8.49794e40 | + | 7.89933e41i | 0.133282 | + | 1.23894i | ||||
\(411\) | −1.18243e41 | −0.178364 | ||||||||
\(412\) | −2.82013e41 | − | 2.82013e41i | −0.409179 | − | 0.409179i | ||||
\(413\) | 8.24519e41 | − | 8.24519e41i | 1.15080 | − | 1.15080i | ||||
\(414\) | 1.33170e41i | 0.178813i | ||||||||
\(415\) | −8.49509e41 | + | 9.13884e40i | −1.09748 | + | 0.118065i | ||||
\(416\) | 6.44635e41 | 0.801347 | ||||||||
\(417\) | 7.26509e41 | + | 7.26509e41i | 0.869088 | + | 0.869088i | ||||
\(418\) | −2.16642e42 | + | 2.16642e42i | −2.49415 | + | 2.49415i | ||||
\(419\) | 1.93654e41i | 0.214586i | 0.994227 | + | 0.107293i | \(0.0342183\pi\) | ||||
−0.994227 | + | 0.107293i | \(0.965782\pi\) | |||||||
\(420\) | 2.09215e42 | − | 2.59655e42i | 2.23154 | − | 2.76955i | ||||
\(421\) | 8.78917e41 | 0.902473 | 0.451237 | − | 0.892404i | \(-0.350983\pi\) | ||||
0.451237 | + | 0.892404i | \(0.350983\pi\) | |||||||
\(422\) | 1.45789e42 | + | 1.45789e42i | 1.44120 | + | 1.44120i | ||||
\(423\) | 1.56095e41 | − | 1.56095e41i | 0.148574 | − | 0.148574i | ||||
\(424\) | − | 2.17371e42i | − | 1.99227i | ||||||
\(425\) | 4.56976e41 | − | 7.11276e41i | 0.403340 | − | 0.627791i | ||||
\(426\) | −3.12044e42 | −2.65254 | ||||||||
\(427\) | −3.35320e41 | − | 3.35320e41i | −0.274545 | − | 0.274545i | ||||
\(428\) | 4.10817e42 | − | 4.10817e42i | 3.24002 | − | 3.24002i | ||||
\(429\) | 5.95848e41i | 0.452709i | ||||||||
\(430\) | 2.96100e42 | + | 2.38580e42i | 2.16742 | + | 1.74638i | ||||
\(431\) | −9.45849e41 | −0.667092 | −0.333546 | − | 0.942734i | \(-0.608245\pi\) | ||||
−0.333546 | + | 0.942734i | \(0.608245\pi\) | |||||||
\(432\) | −2.51856e42 | − | 2.51856e42i | −1.71164 | − | 1.71164i | ||||
\(433\) | −2.36559e41 | + | 2.36559e41i | −0.154929 | + | 0.154929i | −0.780315 | − | 0.625386i | \(-0.784941\pi\) |
0.625386 | + | 0.780315i | \(0.284941\pi\) | |||||||
\(434\) | 3.37974e42i | 2.13328i | ||||||||
\(435\) | 1.30041e41 | + | 1.20880e42i | 0.0791136 | + | 0.735407i | ||||
\(436\) | 2.77557e42 | 1.62768 | ||||||||
\(437\) | 9.75505e41 | + | 9.75505e41i | 0.551476 | + | 0.551476i | ||||
\(438\) | −4.65615e41 | + | 4.65615e41i | −0.253770 | + | 0.253770i | ||||
\(439\) | − | 3.18528e42i | − | 1.67384i | −0.547323 | − | 0.836921i | \(-0.684353\pi\) | ||
0.547323 | − | 0.836921i | \(-0.315647\pi\) | |||||||
\(440\) | −6.62754e42 | + | 7.12978e41i | −3.35822 | + | 0.361271i | ||||
\(441\) | 2.74970e41 | 0.134359 | ||||||||
\(442\) | 7.20593e41 | + | 7.20593e41i | 0.339573 | + | 0.339573i | ||||
\(443\) | 6.98555e41 | − | 6.98555e41i | 0.317498 | − | 0.317498i | −0.530307 | − | 0.847805i | \(-0.677923\pi\) |
0.847805 | + | 0.530307i | \(0.177923\pi\) | |||||||
\(444\) | 1.04459e42i | 0.457951i | ||||||||
\(445\) | −6.58472e41 | + | 8.17225e41i | −0.278469 | + | 0.345606i | ||||
\(446\) | −1.93842e42 | −0.790844 | ||||||||
\(447\) | 4.93820e41 | + | 4.93820e41i | 0.194378 | + | 0.194378i | ||||
\(448\) | −3.91485e42 | + | 3.91485e42i | −1.48685 | + | 1.48685i | ||||
\(449\) | − | 5.89734e41i | − | 0.216130i | −0.994144 | − | 0.108065i | \(-0.965535\pi\) | ||
0.994144 | − | 0.108065i | \(-0.0344654\pi\) | |||||||
\(450\) | −8.53442e41 | − | 5.48314e41i | −0.301838 | − | 0.193923i | ||||
\(451\) | 2.35228e42 | 0.802906 | ||||||||
\(452\) | −3.41320e42 | − | 3.41320e42i | −1.12447 | − | 1.12447i | ||||
\(453\) | −2.97408e42 | + | 2.97408e42i | −0.945761 | + | 0.945761i | ||||
\(454\) | − | 3.29908e42i | − | 1.01274i | ||||||
\(455\) | −1.17894e42 | − | 9.49921e41i | −0.349389 | − | 0.281517i | ||||
\(456\) | 1.67321e43 | 4.78754 | ||||||||
\(457\) | 9.39889e41 | + | 9.39889e41i | 0.259667 | + | 0.259667i | 0.824919 | − | 0.565251i | \(-0.191221\pi\) |
−0.565251 | + | 0.824919i | \(0.691221\pi\) | |||||||
\(458\) | −5.71797e42 | + | 5.71797e42i | −1.52544 | + | 1.52544i | ||||
\(459\) | − | 2.55547e42i | − | 0.658366i | ||||||
\(460\) | 5.35302e41 | + | 4.97594e42i | 0.133191 | + | 1.23808i | ||||
\(461\) | −6.05305e42 | −1.45465 | −0.727327 | − | 0.686291i | \(-0.759237\pi\) | ||||
−0.727327 | + | 0.686291i | \(0.759237\pi\) | |||||||
\(462\) | −9.77531e42 | − | 9.77531e42i | −2.26913 | − | 2.26913i | ||||
\(463\) | −2.11416e42 | + | 2.11416e42i | −0.474070 | + | 0.474070i | −0.903229 | − | 0.429159i | \(-0.858810\pi\) |
0.429159 | + | 0.903229i | \(0.358810\pi\) | |||||||
\(464\) | − | 8.58067e42i | − | 1.85880i | ||||||
\(465\) | 4.53608e42 | − | 4.87983e41i | 0.949366 | − | 0.102131i | ||||
\(466\) | 8.37729e42 | 1.69406 | ||||||||
\(467\) | 5.09474e42 | + | 5.09474e42i | 0.995524 | + | 0.995524i | 0.999990 | − | 0.00446649i | \(-0.00142173\pi\) |
−0.00446649 | + | 0.999990i | \(0.501422\pi\) | |||||||
\(468\) | 6.17473e41 | − | 6.17473e41i | 0.116596 | − | 0.116596i | ||||
\(469\) | − | 1.33218e42i | − | 0.243107i | ||||||
\(470\) | 7.28849e42 | − | 9.04569e42i | 1.28550 | − | 1.59542i | ||||
\(471\) | −4.79748e42 | −0.817859 | ||||||||
\(472\) | 1.50087e43 | + | 1.50087e43i | 2.47327 | + | 2.47327i | ||||
\(473\) | 7.96093e42 | − | 7.96093e42i | 1.26819 | − | 1.26819i | ||||
\(474\) | − | 7.42354e42i | − | 1.14329i | ||||||
\(475\) | −1.02683e43 | + | 2.23515e42i | −1.52897 | + | 0.332819i | ||||
\(476\) | −1.68852e43 | −2.43106 | ||||||||
\(477\) | −6.92542e41 | − | 6.92542e41i | −0.0964166 | − | 0.0964166i | ||||
\(478\) | −7.82197e42 | + | 7.82197e42i | −1.05310 | + | 1.05310i | ||||
\(479\) | 2.06787e42i | 0.269250i | 0.990897 | + | 0.134625i | \(0.0429830\pi\) | ||||
−0.990897 | + | 0.134625i | \(0.957017\pi\) | |||||||
\(480\) | 1.57210e43 | + | 1.26671e43i | 1.97980 | + | 1.59521i | ||||
\(481\) | 4.74286e41 | 0.0577722 | ||||||||
\(482\) | 5.08343e42 | + | 5.08343e42i | 0.598968 | + | 0.598968i | ||||
\(483\) | −4.40167e42 | + | 4.40167e42i | −0.501722 | + | 0.501722i | ||||
\(484\) | 1.02509e43i | 1.13041i | ||||||||
\(485\) | −7.51477e41 | − | 6.98541e42i | −0.0801766 | − | 0.745288i | ||||
\(486\) | −6.86022e42 | −0.708203 | ||||||||
\(487\) | −4.62925e42 | − | 4.62925e42i | −0.462432 | − | 0.462432i | 0.437020 | − | 0.899452i | \(-0.356034\pi\) |
−0.899452 | + | 0.437020i | \(0.856034\pi\) | |||||||
\(488\) | 6.10383e42 | − | 6.10383e42i | 0.590045 | − | 0.590045i | ||||
\(489\) | 1.12431e43i | 1.05183i | ||||||||
\(490\) | 1.43868e43 | − | 1.54770e42i | 1.30265 | − | 0.140136i | ||||
\(491\) | 1.32422e43 | 1.16053 | 0.580266 | − | 0.814427i | \(-0.302949\pi\) | ||||
0.580266 | + | 0.814427i | \(0.302949\pi\) | |||||||
\(492\) | −1.51462e43 | − | 1.51462e43i | −1.28488 | − | 1.28488i | ||||
\(493\) | 4.35321e42 | − | 4.35321e42i | 0.357486 | − | 0.357486i | ||||
\(494\) | − | 1.26672e43i | − | 1.00705i | ||||||
\(495\) | −1.88438e42 | + | 2.33868e42i | −0.145039 | + | 0.180007i | ||||
\(496\) | −3.21993e43 | −2.39960 | ||||||||
\(497\) | −1.65996e43 | − | 1.65996e43i | −1.19783 | − | 1.19783i | ||||
\(498\) | 2.28081e43 | − | 2.28081e43i | 1.59375 | − | 1.59375i | ||||
\(499\) | 2.82701e43i | 1.91302i | 0.291704 | + | 0.956509i | \(0.405778\pi\) | ||||
−0.291704 | + | 0.956509i | \(0.594222\pi\) | |||||||
\(500\) | −3.40933e43 | − | 1.70574e43i | −2.23434 | − | 1.11788i | ||||
\(501\) | 2.79033e43 | 1.77113 | ||||||||
\(502\) | −1.74748e43 | − | 1.74748e43i | −1.07437 | − | 1.07437i | ||||
\(503\) | −4.98530e42 | + | 4.98530e42i | −0.296895 | + | 0.296895i | −0.839797 | − | 0.542901i | \(-0.817326\pi\) |
0.542901 | + | 0.839797i | \(0.317326\pi\) | |||||||
\(504\) | 1.21509e43i | 0.701000i | ||||||||
\(505\) | 2.32827e43 | + | 1.87599e43i | 1.30128 | + | 1.04850i | ||||
\(506\) | 2.07483e43 | 1.12350 | ||||||||
\(507\) | 1.29715e43 | + | 1.29715e43i | 0.680556 | + | 0.680556i | ||||
\(508\) | 2.89304e42 | − | 2.89304e42i | 0.147074 | − | 0.147074i | ||||
\(509\) | 5.33326e42i | 0.262729i | 0.991334 | + | 0.131365i | \(0.0419359\pi\) | ||||
−0.991334 | + | 0.131365i | \(0.958064\pi\) | |||||||
\(510\) | 3.41379e42 | + | 3.17332e43i | 0.162972 | + | 1.51492i | ||||
\(511\) | −4.95379e42 | −0.229194 | ||||||||
\(512\) | 2.04910e43 | + | 2.04910e43i | 0.918848 | + | 0.918848i | ||||
\(513\) | −2.24611e43 | + | 2.24611e43i | −0.976232 | + | 0.976232i | ||||
\(514\) | − | 1.84912e43i | − | 0.779032i | ||||||
\(515\) | −5.63879e42 | + | 6.06610e41i | −0.230288 | + | 0.0247739i | ||||
\(516\) | −1.02520e44 | −4.05894 | ||||||||
\(517\) | −2.43202e43 | − | 2.43202e43i | −0.933507 | − | 0.933507i | ||||
\(518\) | −7.78100e42 | + | 7.78100e42i | −0.289574 | + | 0.289574i | ||||
\(519\) | − | 3.42485e42i | − | 0.123584i | ||||||
\(520\) | 1.72914e43 | − | 2.14602e43i | 0.605030 | − | 0.750898i | ||||
\(521\) | 3.76240e43 | 1.27662 | 0.638309 | − | 0.769780i | \(-0.279634\pi\) | ||||
0.638309 | + | 0.769780i | \(0.279634\pi\) | |||||||
\(522\) | −5.22331e42 | − | 5.22331e42i | −0.171877 | − | 0.171877i | ||||
\(523\) | 1.50259e43 | − | 1.50259e43i | 0.479529 | − | 0.479529i | −0.425452 | − | 0.904981i | \(-0.639885\pi\) |
0.904981 | + | 0.425452i | \(0.139885\pi\) | |||||||
\(524\) | 6.38954e43i | 1.97774i | ||||||||
\(525\) | −1.00854e43 | − | 4.63324e43i | −0.302792 | − | 1.39103i | ||||
\(526\) | 5.61988e43 | 1.63665 | ||||||||
\(527\) | −1.63356e43 | − | 1.63356e43i | −0.461493 | − | 0.461493i | ||||
\(528\) | 9.31310e43 | − | 9.31310e43i | 2.55242 | − | 2.55242i | ||||
\(529\) | 2.82663e43i | 0.751584i | ||||||||
\(530\) | −4.01328e43 | − | 3.23367e43i | −1.03535 | − | 0.834221i | ||||
\(531\) | 9.56354e42 | 0.239390 | ||||||||
\(532\) | 1.48411e44 | + | 1.48411e44i | 3.60480 | + | 3.60480i | ||||
\(533\) | −6.87697e42 | + | 6.87697e42i | −0.162092 | + | 0.162092i | ||||
\(534\) | − | 3.96204e43i | − | 0.906272i | ||||||
\(535\) | −8.83669e42 | − | 8.21421e43i | −0.196168 | − | 1.82350i | ||||
\(536\) | 2.42497e43 | 0.522480 | ||||||||
\(537\) | 1.28344e43 | + | 1.28344e43i | 0.268402 | + | 0.268402i | ||||
\(538\) | −8.15078e43 | + | 8.15078e43i | −1.65456 | + | 1.65456i | ||||
\(539\) | − | 4.28414e43i | − | 0.844196i | ||||||
\(540\) | −1.14572e44 | + | 1.23254e43i | −2.19168 | + | 0.235776i | ||||
\(541\) | −1.25940e43 | −0.233887 | −0.116944 | − | 0.993139i | \(-0.537310\pi\) | ||||
−0.116944 | + | 0.993139i | \(0.537310\pi\) | |||||||
\(542\) | 1.01428e44 | + | 1.01428e44i | 1.82881 | + | 1.82881i | ||||
\(543\) | −2.93937e43 | + | 2.93937e43i | −0.514584 | + | 0.514584i | ||||
\(544\) | − | 1.02233e44i | − | 1.73783i | ||||||
\(545\) | 2.47633e43 | − | 3.07336e43i | 0.408757 | − | 0.507305i | ||||
\(546\) | 5.71569e43 | 0.916191 | ||||||||
\(547\) | −8.84166e43 | − | 8.84166e43i | −1.37638 | − | 1.37638i | −0.850662 | − | 0.525713i | \(-0.823799\pi\) |
−0.525713 | − | 0.850662i | \(-0.676201\pi\) | |||||||
\(548\) | 1.90913e43 | − | 1.90913e43i | 0.288634 | − | 0.288634i | ||||
\(549\) | − | 3.88935e42i | − | 0.0571110i | ||||||
\(550\) | −8.54294e43 | + | 1.32969e44i | −1.21844 | + | 1.89648i | ||||
\(551\) | −7.65244e43 | −1.06017 | ||||||||
\(552\) | −8.01236e43 | − | 8.01236e43i | −1.07829 | − | 1.07829i | ||||
\(553\) | 3.94905e43 | − | 3.94905e43i | 0.516286 | − | 0.516286i | ||||
\(554\) | − | 9.48284e43i | − | 1.20443i | ||||||
\(555\) | 1.15667e43 | + | 9.31974e42i | 0.142732 | + | 0.115005i | ||||
\(556\) | −2.34602e44 | −2.81277 | ||||||||
\(557\) | 9.39482e43 | + | 9.39482e43i | 1.09447 | + | 1.09447i | 0.995045 | + | 0.0994288i | \(0.0317015\pi\) |
0.0994288 | + | 0.995045i | \(0.468298\pi\) | |||||||
\(558\) | −1.96007e43 | + | 1.96007e43i | −0.221883 | + | 0.221883i | ||||
\(559\) | 4.65481e43i | 0.512050i | ||||||||
\(560\) | 3.57956e43 | + | 3.32741e44i | 0.382667 | + | 3.55711i | ||||
\(561\) | 9.44958e43 | 0.981763 | ||||||||
\(562\) | −7.58594e43 | − | 7.58594e43i | −0.765999 | − | 0.765999i | ||||
\(563\) | −1.25127e44 | + | 1.25127e44i | −1.22805 | + | 1.22805i | −0.263352 | + | 0.964700i | \(0.584828\pi\) |
−0.964700 | + | 0.263352i | \(0.915172\pi\) | |||||||
\(564\) | 3.13192e44i | 2.98775i | ||||||||
\(565\) | −6.82463e43 | + | 7.34180e42i | −0.632855 | + | 0.0680813i | ||||
\(566\) | 1.23057e44 | 1.10928 | ||||||||
\(567\) | −1.21531e44 | − | 1.21531e44i | −1.06502 | − | 1.06502i | ||||
\(568\) | 3.02162e44 | − | 3.02162e44i | 2.57435 | − | 2.57435i | ||||
\(569\) | − | 1.10478e44i | − | 0.915124i | −0.889178 | − | 0.457562i | \(-0.848723\pi\) | ||
0.889178 | − | 0.457562i | \(-0.151277\pi\) | |||||||
\(570\) | 2.48911e44 | − | 3.08921e44i | 2.00469 | − | 2.48800i | ||||
\(571\) | 5.02914e43 | 0.393837 | 0.196918 | − | 0.980420i | \(-0.436907\pi\) | ||||
0.196918 | + | 0.980420i | \(0.436907\pi\) | |||||||
\(572\) | −9.62045e43 | − | 9.62045e43i | −0.732587 | − | 0.732587i | ||||
\(573\) | 1.20232e44 | − | 1.20232e44i | 0.890321 | − | 0.890321i | ||||
\(574\) | − | 2.25643e44i | − | 1.62492i | ||||||
\(575\) | 5.98741e43 | + | 3.84676e43i | 0.419328 | + | 0.269407i | ||||
\(576\) | −4.54081e43 | −0.309295 | ||||||||
\(577\) | 7.02072e43 | + | 7.02072e43i | 0.465124 | + | 0.465124i | 0.900331 | − | 0.435207i | \(-0.143325\pi\) |
−0.435207 | + | 0.900331i | \(0.643325\pi\) | |||||||
\(578\) | −9.09619e43 | + | 9.09619e43i | −0.586157 | + | 0.586157i | ||||
\(579\) | 2.49052e44i | 1.56111i | ||||||||
\(580\) | −2.16167e44 | − | 1.74175e44i | −1.31808 | − | 1.06203i | ||||
\(581\) | 2.42661e44 | 1.43940 | ||||||||
\(582\) | 1.87548e44 | + | 1.87548e44i | 1.08229 | + | 1.08229i | ||||
\(583\) | −1.07901e44 | + | 1.07901e44i | −0.605797 | + | 0.605797i | ||||
\(584\) | − | 9.01739e43i | − | 0.492578i | ||||||
\(585\) | −1.32818e42 | − | 1.23463e43i | −0.00705935 | − | 0.0656208i | ||||
\(586\) | −2.14760e43 | −0.111069 | ||||||||
\(587\) | −1.77933e44 | − | 1.77933e44i | −0.895461 | − | 0.895461i | 0.0995692 | − | 0.995031i | \(-0.468254\pi\) |
−0.995031 | + | 0.0995692i | \(0.968254\pi\) | |||||||
\(588\) | −2.75853e44 | + | 2.75853e44i | −1.35095 | + | 1.35095i | ||||
\(589\) | 2.87161e44i | 1.36861i | ||||||||
\(590\) | 5.00377e44 | − | 5.38296e43i | 2.32095 | − | 0.249683i | ||||
\(591\) | −2.97374e44 | −1.34247 | ||||||||
\(592\) | −7.41308e43 | − | 7.41308e43i | −0.325725 | − | 0.325725i | ||||
\(593\) | 1.20920e44 | − | 1.20920e44i | 0.517159 | − | 0.517159i | −0.399552 | − | 0.916711i | \(-0.630834\pi\) |
0.916711 | + | 0.399552i | \(0.130834\pi\) | |||||||
\(594\) | 4.77732e44i | 1.98885i | ||||||||
\(595\) | −1.50648e44 | + | 1.86969e44i | −0.610510 | + | 0.757700i | ||||
\(596\) | −1.59462e44 | −0.629098 | ||||||||
\(597\) | 3.75246e44 | + | 3.75246e44i | 1.44121 | + | 1.44121i | ||||
\(598\) | −6.06584e43 | + | 6.06584e43i | −0.226815 | + | 0.226815i | ||||
\(599\) | − | 1.71232e44i | − | 0.623385i | −0.950183 | − | 0.311692i | \(-0.899104\pi\) | ||
0.950183 | − | 0.311692i | \(-0.100896\pi\) | |||||||
\(600\) | 8.43389e44 | − | 1.83585e44i | 2.98957 | − | 0.650754i | ||||
\(601\) | 3.11518e44 | 1.07521 | 0.537603 | − | 0.843198i | \(-0.319330\pi\) | ||||
0.537603 | + | 0.843198i | \(0.319330\pi\) | |||||||
\(602\) | −7.63654e44 | − | 7.63654e44i | −2.56657 | − | 2.56657i | ||||
\(603\) | 7.72594e42 | − | 7.72594e42i | 0.0252857 | − | 0.0252857i | ||||
\(604\) | − | 9.60379e44i | − | 3.06092i | ||||||
\(605\) | 1.13507e44 | + | 9.14572e43i | 0.352319 | + | 0.283878i | ||||
\(606\) | −1.12878e45 | −3.41231 | ||||||||
\(607\) | 3.42745e44 | + | 3.42745e44i | 1.00914 | + | 1.00914i | 0.999958 | + | 0.00918494i | \(0.00292370\pi\) |
0.00918494 | + | 0.999958i | \(0.497076\pi\) | |||||||
\(608\) | −8.98569e44 | + | 8.98569e44i | −2.57688 | + | 2.57688i | ||||
\(609\) | − | 3.45293e44i | − | 0.964520i | ||||||
\(610\) | −2.18917e43 | − | 2.03496e44i | −0.0595665 | − | 0.553705i | ||||
\(611\) | 1.42202e44 | 0.376916 | ||||||||
\(612\) | −9.79252e43 | − | 9.79252e43i | −0.252855 | − | 0.252855i | ||||
\(613\) | 1.24312e44 | − | 1.24312e44i | 0.312714 | − | 0.312714i | −0.533246 | − | 0.845960i | \(-0.679028\pi\) |
0.845960 | + | 0.533246i | \(0.179028\pi\) | |||||||
\(614\) | − | 2.50026e43i | − | 0.0612761i | ||||||
\(615\) | −3.02845e44 | + | 3.25795e43i | −0.723134 | + | 0.0777933i | ||||
\(616\) | 1.89315e45 | 4.40447 | ||||||||
\(617\) | −5.35295e44 | − | 5.35295e44i | −1.21347 | − | 1.21347i | −0.969876 | − | 0.243599i | \(-0.921672\pi\) |
−0.243599 | − | 0.969876i | \(-0.578328\pi\) | |||||||
\(618\) | 1.51394e44 | − | 1.51394e44i | 0.334420 | − | 0.334420i | ||||
\(619\) | 4.74043e44i | 1.02039i | 0.860058 | + | 0.510196i | \(0.170427\pi\) | ||||
−0.860058 | + | 0.510196i | \(0.829573\pi\) | |||||||
\(620\) | −6.53599e44 | + | 8.11177e44i | −1.37102 | + | 1.70156i | ||||
\(621\) | 2.15115e44 | 0.439750 | ||||||||
\(622\) | 3.07031e44 | + | 3.07031e44i | 0.611698 | + | 0.611698i | ||||
\(623\) | 2.10765e44 | − | 2.10765e44i | 0.409252 | − | 0.409252i | ||||
\(624\) | 5.44543e44i | 1.03057i | ||||||||
\(625\) | −4.93053e44 | + | 2.25327e44i | −0.909522 | + | 0.415655i | ||||
\(626\) | −4.64856e44 | −0.835852 | ||||||||
\(627\) | −8.30564e44 | − | 8.30564e44i | −1.45577 | − | 1.45577i | ||||
\(628\) | 7.74592e44 | − | 7.74592e44i | 1.32348 | − | 1.32348i | ||||
\(629\) | − | 7.52172e43i | − | 0.125287i | ||||||
\(630\) | 2.24339e44 | + | 1.80759e44i | 0.364297 | + | 0.293529i | ||||
\(631\) | −8.03532e44 | −1.27214 | −0.636068 | − | 0.771633i | \(-0.719440\pi\) | ||||
−0.636068 | + | 0.771633i | \(0.719440\pi\) | |||||||
\(632\) | 7.18845e44 | + | 7.18845e44i | 1.10959 | + | 1.10959i | ||||
\(633\) | −5.58927e44 | + | 5.58927e44i | −0.841192 | + | 0.841192i | ||||
\(634\) | − | 1.03379e45i | − | 1.51706i | ||||||
\(635\) | −6.22294e42 | − | 5.78459e43i | −0.00890463 | − | 0.0827738i | ||||
\(636\) | 1.38953e45 | 1.93889 | ||||||||
\(637\) | 1.25248e44 | + | 1.25248e44i | 0.170428 | + | 0.170428i | ||||
\(638\) | −8.13810e44 | + | 8.13810e44i | −1.07992 | + | 1.07992i | ||||
\(639\) | − | 1.92537e44i | − | 0.249173i | ||||||
\(640\) | −5.41226e44 | + | 5.82240e43i | −0.683123 | + | 0.0734890i | ||||
\(641\) | 1.17538e45 | 1.44693 | 0.723467 | − | 0.690359i | \(-0.242547\pi\) | ||||
0.723467 | + | 0.690359i | \(0.242547\pi\) | |||||||
\(642\) | 2.20540e45 | + | 2.20540e45i | 2.64805 | + | 2.64805i | ||||
\(643\) | 1.46375e44 | − | 1.46375e44i | 0.171432 | − | 0.171432i | −0.616176 | − | 0.787608i | \(-0.711319\pi\) |
0.787608 | + | 0.616176i | \(0.211319\pi\) | |||||||
\(644\) | − | 1.42137e45i | − | 1.62380i | ||||||
\(645\) | −9.14672e44 | + | 1.13519e45i | −1.01932 | + | 1.26507i | ||||
\(646\) | −2.00890e45 | −2.18392 | ||||||||
\(647\) | 8.61440e44 | + | 8.61440e44i | 0.913601 | + | 0.913601i | 0.996554 | − | 0.0829525i | \(-0.0264350\pi\) |
−0.0829525 | + | 0.996554i | \(0.526435\pi\) | |||||||
\(648\) | 2.21224e45 | − | 2.21224e45i | 2.28892 | − | 2.28892i | ||||
\(649\) | − | 1.49004e45i | − | 1.50412i | ||||||
\(650\) | −1.38985e44 | − | 6.38496e44i | −0.136884 | − | 0.628847i | ||||
\(651\) | −1.29573e45 | −1.24514 | ||||||||
\(652\) | −1.81529e45 | − | 1.81529e45i | −1.70210 | − | 1.70210i | ||||
\(653\) | 1.32500e45 | − | 1.32500e45i | 1.21228 | − | 1.21228i | 0.242009 | − | 0.970274i | \(-0.422194\pi\) |
0.970274 | − | 0.242009i | \(-0.0778062\pi\) | |||||||
\(654\) | 1.49001e45i | 1.33029i | ||||||||
\(655\) | 7.07508e44 | + | 5.70069e44i | 0.616411 | + | 0.496668i | ||||
\(656\) | 2.14974e45 | 1.82778 | ||||||||
\(657\) | −2.87293e43 | − | 2.87293e43i | −0.0238385 | − | 0.0238385i | ||||
\(658\) | −2.33292e45 | + | 2.33292e45i | −1.88923 | + | 1.88923i | ||||
\(659\) | − | 1.35807e45i | − | 1.07339i | −0.843777 | − | 0.536693i | \(-0.819673\pi\) | ||
0.843777 | − | 0.536693i | \(-0.180327\pi\) | |||||||
\(660\) | −4.55766e44 | − | 4.23661e45i | −0.351592 | − | 3.26825i | ||||
\(661\) | −1.26466e45 | −0.952251 | −0.476125 | − | 0.879377i | \(-0.657959\pi\) | ||||
−0.476125 | + | 0.879377i | \(0.657959\pi\) | |||||||
\(662\) | 1.05159e45 | + | 1.05159e45i | 0.772895 | + | 0.772895i | ||||
\(663\) | −2.76262e44 | + | 2.76262e44i | −0.198200 | + | 0.198200i | ||||
\(664\) | 4.41716e45i | 3.09353i | ||||||||
\(665\) | 2.96746e45 | − | 3.19233e44i | 2.02880 | − | 0.218254i | ||||
\(666\) | −9.02512e43 | −0.0602373 | ||||||||
\(667\) | 3.66446e44 | + | 3.66446e44i | 0.238779 | + | 0.238779i | ||||
\(668\) | −4.50521e45 | + | 4.50521e45i | −2.86610 | + | 2.86610i | ||||
\(669\) | − | 7.43154e44i | − | 0.461595i | ||||||
\(670\) | 3.60745e44 | − | 4.47718e44i | 0.218778 | − | 0.271523i | ||||
\(671\) | −6.05975e44 | −0.358835 | ||||||||
\(672\) | −4.05452e45 | − | 4.05452e45i | −2.34440 | − | 2.34440i | ||||
\(673\) | 1.15935e45 | − | 1.15935e45i | 0.654595 | − | 0.654595i | −0.299501 | − | 0.954096i | \(-0.596820\pi\) |
0.954096 | + | 0.299501i | \(0.0968203\pi\) | |||||||
\(674\) | 4.75023e45i | 2.61913i | ||||||||
\(675\) | −8.85719e44 | + | 1.37861e45i | −0.476909 | + | 0.742301i | ||||
\(676\) | −4.18872e45 | −2.20259 | ||||||||
\(677\) | 6.38384e44 | + | 6.38384e44i | 0.327841 | + | 0.327841i | 0.851765 | − | 0.523924i | \(-0.175532\pi\) |
−0.523924 | + | 0.851765i | \(0.675532\pi\) | |||||||
\(678\) | 1.83232e45 | − | 1.83232e45i | 0.919021 | − | 0.919021i | ||||
\(679\) | 1.99537e45i | 0.977480i | ||||||||
\(680\) | −3.40339e45 | − | 2.74225e45i | −1.62843 | − | 1.31209i | ||||
\(681\) | 1.26480e45 | 0.591112 | ||||||||
\(682\) | 3.05386e45 | + | 3.05386e45i | 1.39411 | + | 1.39411i | ||||
\(683\) | 1.93850e45 | − | 1.93850e45i | 0.864438 | − | 0.864438i | −0.127411 | − | 0.991850i | \(-0.540667\pi\) |
0.991850 | + | 0.127411i | \(0.0406669\pi\) | |||||||
\(684\) | 1.72141e45i | 0.749872i | ||||||||
\(685\) | −4.10655e43 | − | 3.81727e44i | −0.0174754 | − | 0.162444i | ||||
\(686\) | 1.75727e45 | 0.730556 | ||||||||
\(687\) | −2.19216e45 | − | 2.19216e45i | −0.890358 | − | 0.890358i | ||||
\(688\) | 7.27546e45 | − | 7.27546e45i | 2.88699 | − | 2.88699i | ||||
\(689\) | − | 6.30902e44i | − | 0.244599i | ||||||
\(690\) | −2.67125e45 | + | 2.87367e44i | −1.01188 | + | 0.108856i | ||||
\(691\) | −3.70189e45 | −1.37017 | −0.685085 | − | 0.728463i | \(-0.740235\pi\) | ||||
−0.685085 | + | 0.728463i | \(0.740235\pi\) | |||||||
\(692\) | 5.52969e44 | + | 5.52969e44i | 0.199988 | + | 0.199988i | ||||
\(693\) | 6.03156e44 | − | 6.03156e44i | 0.213156 | − | 0.213156i | ||||
\(694\) | − | 5.26028e45i | − | 1.81659i | ||||||
\(695\) | −2.09309e45 | + | 2.59772e45i | −0.706369 | + | 0.876669i | ||||
\(696\) | 6.28537e45 | 2.07292 | ||||||||
\(697\) | 1.09062e45 | + | 1.09062e45i | 0.351520 | + | 0.351520i | ||||
\(698\) | 5.49983e45 | − | 5.49983e45i | 1.73246 | − | 1.73246i | ||||
\(699\) | 3.21169e45i | 0.988778i | ||||||||
\(700\) | 9.10912e45 | + | 5.85238e45i | 2.74099 | + | 1.76102i | ||||
\(701\) | 8.01374e44 | 0.235693 | 0.117847 | − | 0.993032i | \(-0.462401\pi\) | ||||
0.117847 | + | 0.993032i | \(0.462401\pi\) | |||||||
\(702\) | −1.39667e45 | − | 1.39667e45i | −0.401512 | − | 0.401512i | ||||
\(703\) | −6.61116e44 | + | 6.61116e44i | −0.185777 | + | 0.185777i | ||||
\(704\) | 7.07475e45i | 1.94334i | ||||||||
\(705\) | 3.46794e45 | + | 2.79427e45i | 0.931207 | + | 0.750312i | ||||
\(706\) | −3.95504e45 | −1.03819 | ||||||||
\(707\) | −6.00470e45 | − | 6.00470e45i | −1.54092 | − | 1.54092i | ||||
\(708\) | −9.59423e45 | + | 9.59423e45i | −2.40701 | + | 2.40701i | ||||
\(709\) | 3.45331e45i | 0.847023i | 0.905891 | + | 0.423512i | \(0.139203\pi\) | ||||
−0.905891 | + | 0.423512i | \(0.860797\pi\) | |||||||
\(710\) | −1.08372e45 | − | 1.00738e46i | −0.259886 | − | 2.41580i | ||||
\(711\) | 4.58047e44 | 0.107398 | ||||||||
\(712\) | 3.83656e45 | + | 3.83656e45i | 0.879554 | + | 0.879554i | ||||
\(713\) | 1.37510e45 | − | 1.37510e45i | 0.308250 | − | 0.308250i | ||||
\(714\) | − | 9.06453e45i | − | 1.98689i | ||||||
\(715\) | −1.92359e45 | + | 2.06936e44i | −0.412303 | + | 0.0443547i | ||||
\(716\) | −4.14442e45 | −0.868672 | ||||||||
\(717\) | −2.99879e45 | − | 2.99879e45i | −0.614667 | − | 0.614667i | ||||
\(718\) | −5.57455e45 | + | 5.57455e45i | −1.11743 | + | 1.11743i | ||||
\(719\) | − | 5.70040e45i | − | 1.11749i | −0.829340 | − | 0.558745i | \(-0.811283\pi\) | ||
0.829340 | − | 0.558745i | \(-0.188717\pi\) | |||||||
\(720\) | −1.72212e45 | + | 2.13731e45i | −0.330175 | + | 0.409777i | ||||
\(721\) | 1.61071e45 | 0.302033 | ||||||||
\(722\) | 1.04457e46 | + | 1.04457e46i | 1.91577 | + | 1.91577i | ||||
\(723\) | −1.94889e45 | + | 1.94889e45i | −0.349602 | + | 0.349602i | ||||
\(724\) | − | 9.49170e45i | − | 1.66543i | ||||||
\(725\) | −3.85725e45 | + | 8.39627e44i | −0.662018 | + | 0.144105i | ||||
\(726\) | −5.50299e45 | −0.923874 | ||||||||
\(727\) | −4.55645e43 | − | 4.55645e43i | −0.00748300 | − | 0.00748300i | 0.703355 | − | 0.710838i | \(-0.251684\pi\) |
−0.710838 | + | 0.703355i | \(0.751684\pi\) | |||||||
\(728\) | −5.53468e45 | + | 5.53468e45i | −0.889182 | + | 0.889182i | ||||
\(729\) | 4.71896e45i | 0.741661i | ||||||||
\(730\) | −1.66486e45 | − | 1.34145e45i | −0.255984 | − | 0.206257i | ||||
\(731\) | 7.38208e45 | 1.11045 | ||||||||
\(732\) | 3.90183e45 | + | 3.90183e45i | 0.574237 | + | 0.574237i | ||||
\(733\) | −1.81150e45 | + | 1.81150e45i | −0.260841 | + | 0.260841i | −0.825395 | − | 0.564555i | \(-0.809048\pi\) |
0.564555 | + | 0.825395i | \(0.309048\pi\) | |||||||
\(734\) | − | 1.83228e46i | − | 2.58140i | ||||||
\(735\) | 5.93360e44 | + | 5.51562e45i | 0.0817939 | + | 0.760322i | ||||
\(736\) | 8.60581e45 | 1.16077 | ||||||||
\(737\) | −1.20373e45 | − | 1.20373e45i | −0.158873 | − | 0.158873i | ||||
\(738\) | 1.30861e45 | − | 1.30861e45i | 0.169008 | − | 0.169008i | ||||
\(739\) | 1.85724e45i | 0.234724i | 0.993089 | + | 0.117362i | \(0.0374438\pi\) | ||||
−0.993089 | + | 0.117362i | \(0.962556\pi\) | |||||||
\(740\) | −3.37228e45 | + | 3.62783e44i | −0.417077 | + | 0.0448683i | ||||
\(741\) | 4.85636e45 | 0.587786 | ||||||||
\(742\) | 1.03504e46 | + | 1.03504e46i | 1.22601 | + | 1.22601i | ||||
\(743\) | 8.67590e45 | − | 8.67590e45i | 1.00576 | − | 1.00576i | 0.00577436 | − | 0.999983i | \(-0.498162\pi\) |
0.999983 | − | 0.00577436i | \(-0.00183805\pi\) | |||||||
\(744\) | − | 2.35861e46i | − | 2.67602i | ||||||
\(745\) | −1.42271e45 | + | 1.76571e45i | −0.157985 | + | 0.196074i | ||||
\(746\) | −2.57976e46 | −2.80387 | ||||||||
\(747\) | 1.40730e45 | + | 1.40730e45i | 0.149713 | + | 0.149713i | ||||
\(748\) | −1.52571e46 | + | 1.52571e46i | −1.58872 | + | 1.58872i | ||||
\(749\) | 2.34638e46i | 2.39160i | ||||||||
\(750\) | 9.15699e45 | − | 1.83024e46i | 0.913634 | − | 1.82611i | ||||
\(751\) | 3.45624e45 | 0.337570 | 0.168785 | − | 0.985653i | \(-0.446016\pi\) | ||||
0.168785 | + | 0.985653i | \(0.446016\pi\) | |||||||
\(752\) | −2.22261e46 | − | 2.22261e46i | −2.12509 | − | 2.12509i | ||||
\(753\) | 6.69952e45 | − | 6.69952e45i | 0.627082 | − | 0.627082i | ||||
\(754\) | − | 4.75840e45i | − | 0.436033i | ||||||
\(755\) | −1.06342e46 | − | 8.56841e45i | −0.954011 | − | 0.768687i | ||||
\(756\) | 3.27272e46 | 2.87449 | ||||||||
\(757\) | −7.48021e45 | − | 7.48021e45i | −0.643250 | − | 0.643250i | 0.308103 | − | 0.951353i | \(-0.400306\pi\) |
−0.951353 | + | 0.308103i | \(0.900306\pi\) | |||||||
\(758\) | −5.05057e45 | + | 5.05057e45i | −0.425239 | + | 0.425239i | ||||
\(759\) | 7.95451e45i | 0.655760i | ||||||||
\(760\) | 5.81100e45 | + | 5.40167e46i | 0.469066 | + | 4.36024i | ||||
\(761\) | 1.94002e46 | 1.53338 | 0.766692 | − | 0.642015i | \(-0.221901\pi\) | ||||
0.766692 | + | 0.642015i | \(0.221901\pi\) | |||||||
\(762\) | 1.55308e45 | + | 1.55308e45i | 0.120203 | + | 0.120203i | ||||
\(763\) | −7.92631e45 | + | 7.92631e45i | −0.600729 | + | 0.600729i | ||||
\(764\) | 3.88249e46i | 2.88149i | ||||||||
\(765\) | −1.95800e45 | + | 2.10637e44i | −0.142308 | + | 0.0153092i | ||||
\(766\) | 3.10900e46 | 2.21289 | ||||||||
\(767\) | 4.35617e45 | + | 4.35617e45i | 0.303654 | + | 0.303654i | ||||
\(768\) | −3.70218e45 | + | 3.70218e45i | −0.252743 | + | 0.252743i | ||||
\(769\) | − | 9.03883e45i | − | 0.604353i | −0.953252 | − | 0.302176i | \(-0.902287\pi\) | ||
0.953252 | − | 0.302176i | \(-0.0977132\pi\) | |||||||
\(770\) | 2.81630e46 | − | 3.49528e46i | 1.84428 | − | 2.28892i | ||||
\(771\) | 7.08917e45 | 0.454700 | ||||||||
\(772\) | −4.02115e46 | − | 4.02115e46i | −2.52623 | − | 2.52623i | ||||
\(773\) | 3.46674e44 | − | 3.46674e44i | 0.0213329 | − | 0.0213329i | −0.696360 | − | 0.717693i | \(-0.745198\pi\) |
0.717693 | + | 0.696360i | \(0.245198\pi\) | |||||||
\(774\) | − | 8.85757e45i | − | 0.533899i | ||||||
\(775\) | 3.15074e45 | + | 1.44745e46i | 0.186031 | + | 0.854626i | ||||
\(776\) | −3.63218e46 | −2.10078 | ||||||||
\(777\) | −2.98309e45 | − | 2.98309e45i | −0.169017 | − | 0.169017i | ||||
\(778\) | 1.58430e46 | − | 1.58430e46i | 0.879353 | − | 0.879353i | ||||
\(779\) | − | 1.91719e46i | − | 1.04247i | ||||||
\(780\) | 1.37183e46 | + | 1.10534e46i | 0.730781 | + | 0.588821i | ||||
\(781\) | −2.99980e46 | −1.56558 | ||||||||
\(782\) | 9.61984e45 | + | 9.61984e45i | 0.491881 | + | 0.491881i | ||||
\(783\) | −8.43746e45 | + | 8.43746e45i | −0.422692 | + | 0.422692i | ||||
\(784\) | − | 3.91526e46i | − | 1.92178i | ||||||
\(785\) | −1.66615e45 | − | 1.54878e46i | −0.0801308 | − | 0.744862i | ||||
\(786\) | −3.43011e46 | −1.61639 | ||||||||
\(787\) | 1.53990e46 | + | 1.53990e46i | 0.711047 | + | 0.711047i | 0.966754 | − | 0.255708i | \(-0.0823084\pi\) |
−0.255708 | + | 0.966754i | \(0.582308\pi\) | |||||||
\(788\) | 4.80135e46 | − | 4.80135e46i | 2.17242 | − | 2.17242i | ||||
\(789\) | 2.15455e46i | 0.955267i | ||||||||
\(790\) | 2.39656e46 | − | 2.57817e45i | 1.04125 | − | 0.112016i | ||||
\(791\) | 1.94945e46 | 0.830019 | ||||||||
\(792\) | 1.09792e46 | + | 1.09792e46i | 0.458110 | + | 0.458110i | ||||
\(793\) | 1.77159e45 | − | 1.77159e45i | 0.0724422 | − | 0.0724422i | ||||
\(794\) | 8.49564e46i | 3.40461i | ||||||||
\(795\) | 1.23973e46 | − | 1.53861e46i | 0.486913 | − | 0.604304i | ||||
\(796\) | −1.21173e47 | −4.66442 | ||||||||
\(797\) | −2.93881e46 | − | 2.93881e46i | −1.10876 | − | 1.10876i | −0.993314 | − | 0.115448i | \(-0.963170\pi\) |
−0.115448 | − | 0.993314i | \(-0.536830\pi\) | |||||||
\(798\) | −7.96720e46 | + | 7.96720e46i | −2.94618 | + | 2.94618i | ||||
\(799\) | − | 2.25518e46i | − | 0.817397i | ||||||
\(800\) | −3.54337e46 | + | 5.51519e46i | −1.25886 | + | 1.95939i | ||||
\(801\) | 2.44465e45 | 0.0851328 | ||||||||
\(802\) | 7.69784e46 | + | 7.69784e46i | 2.62772 | + | 2.62772i | ||||
\(803\) | −4.47614e45 | + | 4.47614e45i | −0.149780 | + | 0.149780i | ||||
\(804\) | 1.55015e46i | 0.508483i | ||||||||
\(805\) | −1.57387e46 | − | 1.26813e46i | −0.506099 | − | 0.407785i | ||||
\(806\) | −1.78561e46 | −0.562893 | ||||||||
\(807\) | −3.12485e46 | − | 3.12485e46i | −0.965724 | − | 0.965724i | ||||
\(808\) | 1.09304e47 | − | 1.09304e47i | 3.31171 | − | 3.31171i | ||||
\(809\) | − | 3.79529e46i | − | 1.12738i | −0.825988 | − | 0.563688i | \(-0.809382\pi\) | ||
0.825988 | − | 0.563688i | \(-0.190618\pi\) | |||||||
\(810\) | −7.93430e45 | − | 7.37539e46i | −0.231072 | − | 2.14795i | ||||
\(811\) | 6.69310e46 | 1.91114 | 0.955572 | − | 0.294758i | \(-0.0952390\pi\) | ||||
0.955572 | + | 0.294758i | \(0.0952390\pi\) | |||||||
\(812\) | 5.57504e46 | + | 5.57504e46i | 1.56082 | + | 1.56082i | ||||
\(813\) | −3.88854e46 | + | 3.88854e46i | −1.06743 | + | 1.06743i | ||||
\(814\) | 1.40615e46i | 0.378478i | ||||||||
\(815\) | −3.62965e46 | + | 3.90470e45i | −0.957950 | + | 0.103054i | ||||
\(816\) | 8.63593e46 | 2.23494 | ||||||||
\(817\) | −6.48842e46 | − | 6.48842e46i | −1.64659 | − | 1.64659i | ||||
\(818\) | −3.15282e46 | + | 3.15282e46i | −0.784596 | + | 0.784596i | ||||
\(819\) | 3.52669e45i | 0.0860647i | ||||||||
\(820\) | 4.36366e46 | − | 5.41571e46i | 1.04431 | − | 1.29608i | ||||
\(821\) | 3.26928e46 | 0.767293 | 0.383646 | − | 0.923480i | \(-0.374668\pi\) | ||||
0.383646 | + | 0.923480i | \(0.374668\pi\) | |||||||
\(822\) | 1.02488e46 | + | 1.02488e46i | 0.235899 | + | 0.235899i | ||||
\(823\) | 5.18274e46 | − | 5.18274e46i | 1.16994 | − | 1.16994i | 0.187711 | − | 0.982224i | \(-0.439893\pi\) |
0.982224 | − | 0.187711i | \(-0.0601069\pi\) | |||||||
\(824\) | 2.93198e46i | 0.649122i | ||||||||
\(825\) | −5.09779e46 | − | 3.27520e46i | −1.10693 | − | 0.711172i | ||||
\(826\) | −1.42932e47 | −3.04403 | ||||||||
\(827\) | 2.59262e46 | + | 2.59262e46i | 0.541564 | + | 0.541564i | 0.923987 | − | 0.382423i | \(-0.124910\pi\) |
−0.382423 | + | 0.923987i | \(0.624910\pi\) | |||||||
\(828\) | 8.24319e45 | − | 8.24319e45i | 0.168892 | − | 0.168892i | ||||
\(829\) | 7.51083e46i | 1.50944i | 0.656047 | + | 0.754720i | \(0.272227\pi\) | ||||
−0.656047 | + | 0.754720i | \(0.727773\pi\) | |||||||
\(830\) | 8.15532e46 | + | 6.57108e46i | 1.60765 | + | 1.29535i | ||||
\(831\) | 3.63554e46 | 0.702995 | ||||||||
\(832\) | −2.06833e46 | − | 2.06833e46i | −0.392325 | − | 0.392325i | ||||
\(833\) | 1.98632e46 | − | 1.98632e46i | 0.369597 | − | 0.369597i | ||||
\(834\) | − | 1.25942e47i | − | 2.29886i | ||||||
\(835\) | 9.69072e45 | + | 9.00809e46i | 0.173529 | + | 1.61305i | ||||
\(836\) | 2.68203e47 | 4.71154 | ||||||||
\(837\) | 3.16619e46 | + | 3.16619e46i | 0.545670 | + | 0.545670i | ||||
\(838\) | 1.67851e46 | − | 1.67851e46i | 0.283805 | − | 0.283805i | ||||
\(839\) | 2.57343e46i | 0.426895i | 0.976955 | + | 0.213447i | \(0.0684692\pi\) | ||||
−0.976955 | + | 0.213447i | \(0.931531\pi\) | |||||||
\(840\) | −2.43734e47 | + | 2.62204e46i | −3.96686 | + | 0.426747i | ||||
\(841\) | 3.38771e46 | 0.540966 | ||||||||
\(842\) | −7.61810e46 | − | 7.61810e46i | −1.19358 | − | 1.19358i | ||||
\(843\) | 2.90830e46 | − | 2.90830e46i | 0.447094 | − | 0.447094i | ||||
\(844\) | − | 1.80487e47i | − | 2.72249i | ||||||
\(845\) | −3.73714e46 | + | 4.63813e46i | −0.553136 | + | 0.686492i | ||||
\(846\) | −2.70593e46 | −0.392999 | ||||||||
\(847\) | −2.92738e46 | − | 2.92738e46i | −0.417201 | − | 0.417201i | ||||
\(848\) | −9.86099e46 | + | 9.86099e46i | −1.37907 | + | 1.37907i | ||||
\(849\) | 4.71776e46i | 0.647459i | ||||||||
\(850\) | −1.01259e47 | + | 2.20417e46i | −1.36374 | + | 0.296853i | ||||
\(851\) | 6.33167e45 | 0.0836845 | ||||||||
\(852\) | 1.93155e47 | + | 1.93155e47i | 2.50538 | + | 2.50538i | ||||
\(853\) | −7.81000e46 | + | 7.81000e46i | −0.994183 | + | 0.994183i | −0.999983 | − | 0.00580004i | \(-0.998154\pi\) |
0.00580004 | + | 0.999983i | \(0.498154\pi\) | |||||||
\(854\) | 5.81283e46i | 0.726210i | ||||||||
\(855\) | 1.90610e46 | + | 1.53583e46i | 0.233716 | + | 0.188315i | ||||
\(856\) | −4.27111e47 | −5.13998 | ||||||||
\(857\) | 1.49990e46 | + | 1.49990e46i | 0.177161 | + | 0.177161i | 0.790117 | − | 0.612956i | \(-0.210020\pi\) |
−0.612956 | + | 0.790117i | \(0.710020\pi\) | |||||||
\(858\) | 5.16457e46 | − | 5.16457e46i | 0.598739 | − | 0.598739i | ||||
\(859\) | 8.62393e46i | 0.981329i | 0.871348 | + | 0.490665i | \(0.163246\pi\) | ||||
−0.871348 | + | 0.490665i | \(0.836754\pi\) | |||||||
\(860\) | −3.56048e46 | − | 3.30967e47i | −0.397679 | − | 3.69666i | ||||
\(861\) | 8.65073e46 | 0.948424 | ||||||||
\(862\) | 8.19824e46 | + | 8.19824e46i | 0.882276 | + | 0.882276i | ||||
\(863\) | −1.52033e46 | + | 1.52033e46i | −0.160607 | + | 0.160607i | −0.782836 | − | 0.622228i | \(-0.786227\pi\) |
0.622228 | + | 0.782836i | \(0.286227\pi\) | |||||||
\(864\) | 1.98150e47i | 2.05482i | ||||||||
\(865\) | 1.10565e46 | − | 1.18944e45i | 0.112554 | − | 0.0121083i | ||||
\(866\) | 4.10079e46 | 0.409809 | ||||||||
\(867\) | −3.48730e46 | − | 3.48730e46i | −0.342124 | − | 0.342124i | ||||
\(868\) | 2.09206e47 | − | 2.09206e47i | 2.01492 | − | 2.01492i | ||||
\(869\) | − | 7.13654e46i | − | 0.674794i | ||||||
\(870\) | 9.35028e46 | − | 1.16046e47i | 0.867994 | − | 1.07726i | ||||
\(871\) | 7.03829e45 | 0.0641470 | ||||||||
\(872\) | −1.44283e47 | − | 1.44283e47i | −1.29107 | − | 1.29107i | ||||
\(873\) | −1.15721e46 | + | 1.15721e46i | −0.101668 | + | 0.101668i | ||||
\(874\) | − | 1.69106e47i | − | 1.45873i | ||||||
\(875\) | 1.46074e47 | − | 4.86501e46i | 1.23721 | − | 0.412055i | ||||
\(876\) | 5.76431e46 | 0.479382 | ||||||||
\(877\) | −5.23615e46 | − | 5.23615e46i | −0.427581 | − | 0.427581i | 0.460223 | − | 0.887804i | \(-0.347770\pi\) |
−0.887804 | + | 0.460223i | \(0.847770\pi\) | |||||||
\(878\) | −2.76087e47 | + | 2.76087e47i | −2.21377 | + | 2.21377i | ||||
\(879\) | − | 8.23349e45i | − | 0.0648279i | ||||||
\(880\) | 3.33001e47 | + | 2.68313e47i | 2.57468 | + | 2.07453i | ||||
\(881\) | −8.74229e46 | −0.663759 | −0.331880 | − | 0.943322i | \(-0.607683\pi\) | ||||
−0.331880 | + | 0.943322i | \(0.607683\pi\) | |||||||
\(882\) | −2.38333e46 | − | 2.38333e46i | −0.177700 | − | 0.177700i | ||||
\(883\) | 1.79302e47 | − | 1.79302e47i | 1.31284 | − | 1.31284i | 0.393532 | − | 0.919311i | \(-0.371253\pi\) |
0.919311 | − | 0.393532i | \(-0.128747\pi\) | |||||||
\(884\) | − | 8.92094e46i | − | 0.641467i | ||||||
\(885\) | 2.06372e46 | + | 1.91835e47i | 0.145733 | + | 1.35468i | ||||
\(886\) | −1.21096e47 | −0.839827 | ||||||||
\(887\) | 9.75192e46 | + | 9.75192e46i | 0.664220 | + | 0.664220i | 0.956372 | − | 0.292152i | \(-0.0943713\pi\) |
−0.292152 | + | 0.956372i | \(0.594371\pi\) | |||||||
\(888\) | 5.43011e46 | − | 5.43011e46i | 0.363246 | − | 0.363246i | ||||
\(889\) | 1.65236e46i | 0.108562i | ||||||||
\(890\) | 1.27907e47 | − | 1.37600e46i | 0.825384 | − | 0.0887931i | ||||
\(891\) | −2.19626e47 | −1.39201 | ||||||||
\(892\) | 1.19988e47 | + | 1.19988e47i | 0.746967 | + | 0.746967i | ||||
\(893\) | −1.98217e47 | + | 1.98217e47i | −1.21204 | + | 1.21204i | ||||
\(894\) | − | 8.56046e46i | − | 0.514158i | ||||||
\(895\) | −3.69762e46 | + | 4.58908e46i | −0.218149 | + | 0.270743i | ||||
\(896\) | 1.54600e47 | 0.895947 | ||||||||
\(897\) | −2.32553e46 | − | 2.32553e46i | −0.132386 | − | 0.132386i | ||||
\(898\) | −5.11158e46 | + | 5.11158e46i | −0.285847 | + | 0.285847i | ||||
\(899\) | 1.07871e47i | 0.592585i | ||||||||
\(900\) | 1.88874e46 | + | 8.67687e46i | 0.101928 | + | 0.468255i | ||||
\(901\) | −1.00055e47 | −0.530447 | ||||||||
\(902\) | −2.03886e47 | − | 2.03886e47i | −1.06190 | − | 1.06190i | ||||
\(903\) | 2.92770e47 | − | 2.92770e47i | 1.49804 | − | 1.49804i | ||||
\(904\) | 3.54858e47i | 1.78386i | ||||||||
\(905\) | −1.05101e47 | − | 8.46840e46i | −0.519073 | − | 0.418239i | ||||
\(906\) | 5.15563e47 | 2.50167 | ||||||||
\(907\) | 1.27332e46 | + | 1.27332e46i | 0.0607047 | + | 0.0607047i | 0.736807 | − | 0.676103i | \(-0.236332\pi\) |
−0.676103 | + | 0.736807i | \(0.736332\pi\) | |||||||
\(908\) | −2.04213e47 | + | 2.04213e47i | −0.956555 | + | 0.956555i | ||||
\(909\) | − | 6.96481e46i | − | 0.320544i | ||||||
\(910\) | 1.98504e46 | + | 1.84521e47i | 0.0897650 | + | 0.834418i | ||||
\(911\) | −3.85412e47 | −1.71250 | −0.856252 | − | 0.516559i | \(-0.827213\pi\) | ||||
−0.856252 | + | 0.516559i | \(0.827213\pi\) | |||||||
\(912\) | −7.59048e47 | − | 7.59048e47i | −3.31400 | − | 3.31400i | ||||
\(913\) | 2.19263e47 | − | 2.19263e47i | 0.940661 | − | 0.940661i | ||||
\(914\) | − | 1.62932e47i | − | 0.686857i | ||||||
\(915\) | 7.80164e46 | − | 8.39285e45i | 0.323183 | − | 0.0347674i | ||||
\(916\) | 7.07885e47 | 2.88161 | ||||||||
\(917\) | −1.82469e47 | − | 1.82469e47i | −0.729927 | − | 0.729927i | ||||
\(918\) | −2.21498e47 | + | 2.21498e47i | −0.870736 | + | 0.870736i | ||||
\(919\) | − | 3.61027e47i | − | 1.39473i | −0.716715 | − | 0.697367i | \(-0.754355\pi\) | ||
0.716715 | − | 0.697367i | \(-0.245645\pi\) | |||||||
\(920\) | 2.30839e47 | − | 2.86492e47i | 0.876402 | − | 1.08770i | ||||
\(921\) | 9.58551e45 | 0.0357652 | ||||||||
\(922\) | 5.24654e47 | + | 5.24654e47i | 1.92388 | + | 1.92388i | ||||
\(923\) | 8.77002e46 | − | 8.77002e46i | 0.316063 | − | 0.316063i | ||||
\(924\) | 1.21018e48i | 4.28647i | ||||||||
\(925\) | −2.60701e46 | + | 4.05777e46i | −0.0907559 | + | 0.141260i | ||||
\(926\) | 3.66494e47 | 1.25398 | ||||||||
\(927\) | 9.34127e45 | + | 9.34127e45i | 0.0314145 | + | 0.0314145i | ||||
\(928\) | −3.37545e47 | + | 3.37545e47i | −1.11574 | + | 1.11574i | ||||
\(929\) | 1.36379e47i | 0.443094i | 0.975150 | + | 0.221547i | \(0.0711107\pi\) | ||||
−0.975150 | + | 0.221547i | \(0.928889\pi\) | |||||||
\(930\) | −4.35466e47 | − | 3.50873e47i | −1.39068 | − | 1.12053i | ||||
\(931\) | −3.49172e47 | −1.09608 | ||||||||
\(932\) | −5.18554e47 | − | 5.18554e47i | −1.60007 | − | 1.60007i | ||||
\(933\) | −1.17710e47 | + | 1.17710e47i | −0.357032 | + | 0.357032i | ||||
\(934\) | − | 8.83182e47i | − | 2.63330i | ||||||
\(935\) | 3.28181e46 | + | 3.05063e47i | 0.0961895 | + | 0.894137i | ||||
\(936\) | −6.41963e46 | −0.184968 | ||||||||
\(937\) | 3.45596e47 | + | 3.45596e47i | 0.978892 | + | 0.978892i | 0.999782 | − | 0.0208899i | \(-0.00664994\pi\) |
−0.0208899 | + | 0.999782i | \(0.506650\pi\) | |||||||
\(938\) | −1.15468e47 | + | 1.15468e47i | −0.321526 | + | 0.321526i | ||||
\(939\) | − | 1.78217e47i | − | 0.487865i | ||||||
\(940\) | −1.01109e48 | + | 1.08771e47i | −2.72108 | + | 0.292729i | ||||
\(941\) | 1.34267e47 | 0.355252 | 0.177626 | − | 0.984098i | \(-0.443158\pi\) | ||||
0.177626 | + | 0.984098i | \(0.443158\pi\) | |||||||
\(942\) | 4.15826e47 | + | 4.15826e47i | 1.08168 | + | 1.08168i | ||||
\(943\) | −9.18069e46 | + | 9.18069e46i | −0.234795 | + | 0.234795i | ||||
\(944\) | − | 1.36174e48i | − | 3.42406i | ||||||
\(945\) | 2.91989e47 | − | 3.62386e47i | 0.721868 | − | 0.895905i | ||||
\(946\) | −1.38004e48 | −3.35455 | ||||||||
\(947\) | 2.98340e47 | + | 2.98340e47i | 0.713036 | + | 0.713036i | 0.967169 | − | 0.254134i | \(-0.0817903\pi\) |
−0.254134 | + | 0.967169i | \(0.581790\pi\) | |||||||
\(948\) | −4.59517e47 | + | 4.59517e47i | −1.07986 | + | 1.07986i | ||||
\(949\) | − | 2.61723e46i | − | 0.0604758i | ||||||
\(950\) | 1.08375e48 | + | 6.96278e47i | 2.46235 | + | 1.58200i | ||||
\(951\) | 3.96334e47 | 0.885468 | ||||||||
\(952\) | 8.77747e47 | + | 8.77747e47i | 1.92832 | + | 1.92832i | ||||
\(953\) | −7.84540e46 | + | 7.84540e46i | −0.169484 | + | 0.169484i | −0.786753 | − | 0.617269i | \(-0.788239\pi\) |
0.617269 | + | 0.786753i | \(0.288239\pi\) | |||||||
\(954\) | 1.20053e47i | 0.255036i | ||||||||
\(955\) | 4.29905e47 | + | 3.46392e47i | 0.898087 | + | 0.723626i | ||||
\(956\) | 9.68359e47 | 1.98935 | ||||||||
\(957\) | −3.11999e47 | − | 3.11999e47i | −0.630322 | − | 0.630322i | ||||
\(958\) | 1.79235e47 | − | 1.79235e47i | 0.356102 | − | 0.356102i | ||||
\(959\) | 1.09040e47i | 0.213053i | ||||||||
\(960\) | −9.79864e46 | − | 9.10840e47i | −0.188289 | − | 1.75026i | ||||
\(961\) | −1.24353e47 | −0.235008 | ||||||||
\(962\) | −4.11092e46 | − | 4.11092e46i | −0.0764078 | − | 0.0764078i | ||||
\(963\) | −1.36077e47 | + | 1.36077e47i | −0.248751 | + | 0.248751i | ||||
\(964\) | − | 6.29328e47i | − | 1.13147i | ||||||
\(965\) | −8.04021e47 | + | 8.64950e46i | −1.42177 | + | 0.152952i | ||||
\(966\) | 7.63038e47 | 1.32713 | ||||||||
\(967\) | 7.72425e46 | + | 7.72425e46i | 0.132140 | + | 0.132140i | 0.770083 | − | 0.637944i | \(-0.220215\pi\) |
−0.637944 | + | 0.770083i | \(0.720215\pi\) | |||||||
\(968\) | 5.32872e47 | − | 5.32872e47i | 0.896638 | − | 0.896638i | ||||
\(969\) | − | 7.70172e47i | − | 1.27470i | ||||||
\(970\) | −5.40332e47 | + | 6.70602e47i | −0.879657 | + | 1.09174i | ||||
\(971\) | 3.41064e47 | 0.546170 | 0.273085 | − | 0.961990i | \(-0.411956\pi\) | ||||
0.273085 | + | 0.961990i | \(0.411956\pi\) | |||||||
\(972\) | 4.24647e47 | + | 4.24647e47i | 0.668910 | + | 0.668910i | ||||
\(973\) | 6.69962e47 | − | 6.69962e47i | 1.03811 | − | 1.03811i | ||||
\(974\) | 8.02490e47i | 1.22320i | ||||||||
\(975\) | 2.44787e47 | − | 5.32841e46i | 0.367041 | − | 0.0798957i | ||||
\(976\) | −5.53798e47 | −0.816873 | ||||||||
\(977\) | 2.60278e47 | + | 2.60278e47i | 0.377681 | + | 0.377681i | 0.870265 | − | 0.492584i | \(-0.163948\pi\) |
−0.492584 | + | 0.870265i | \(0.663948\pi\) | |||||||
\(978\) | 9.74509e47 | − | 9.74509e47i | 1.39112 | − | 1.39112i | ||||
\(979\) | − | 3.80886e47i | − | 0.534899i | ||||||
\(980\) | −9.86346e47 | − | 7.94740e47i | −1.36274 | − | 1.09801i | ||||
\(981\) | −9.19367e46 | −0.124964 | ||||||||
\(982\) | −1.14778e48 | − | 1.14778e48i | −1.53488 | − | 1.53488i | ||||
\(983\) | −2.59694e47 | + | 2.59694e47i | −0.341670 | + | 0.341670i | −0.856995 | − | 0.515325i | \(-0.827671\pi\) |
0.515325 | + | 0.856995i | \(0.327671\pi\) | |||||||
\(984\) | 1.57469e48i | 2.03833i | ||||||||
\(985\) | −1.03277e47 | − | 9.60022e47i | −0.131530 | − | 1.22265i | ||||
\(986\) | −7.54637e47 | −0.945600 | ||||||||
\(987\) | −8.94396e47 | − | 8.94396e47i | −1.10269 | − | 1.10269i | ||||
\(988\) | −7.84099e47 | + | 7.84099e47i | −0.951173 | + | 0.951173i | ||||
\(989\) | 6.21412e47i | 0.741718i | ||||||||
\(990\) | 3.66038e47 | − | 3.93776e46i | 0.429895 | − | 0.0462473i | ||||
\(991\) | −1.17065e47 | −0.135285 | −0.0676424 | − | 0.997710i | \(-0.521548\pi\) | ||||
−0.0676424 | + | 0.997710i | \(0.521548\pi\) | |||||||
\(992\) | 1.26665e48 | + | 1.26665e48i | 1.44036 | + | 1.44036i | ||||
\(993\) | −4.03161e47 | + | 4.03161e47i | −0.451118 | + | 0.451118i | ||||
\(994\) | 2.87757e48i | 3.16843i | ||||||||
\(995\) | −1.08110e48 | + | 1.34174e48i | −1.17137 | + | 1.45378i | ||||
\(996\) | −2.82364e48 | −3.01065 | ||||||||
\(997\) | 2.38089e47 | + | 2.38089e47i | 0.249814 | + | 0.249814i | 0.820894 | − | 0.571080i | \(-0.193475\pi\) |
−0.571080 | + | 0.820894i | \(0.693475\pi\) | |||||||
\(998\) | 2.45034e48 | − | 2.45034e48i | 2.53010 | − | 2.53010i | ||||
\(999\) | 1.45787e47i | 0.148140i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5.33.c.a.2.1 | ✓ | 30 | |
5.2 | odd | 4 | 25.33.c.b.18.15 | 30 | |||
5.3 | odd | 4 | inner | 5.33.c.a.3.1 | yes | 30 | |
5.4 | even | 2 | 25.33.c.b.7.15 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.33.c.a.2.1 | ✓ | 30 | 1.1 | even | 1 | trivial | |
5.33.c.a.3.1 | yes | 30 | 5.3 | odd | 4 | inner | |
25.33.c.b.7.15 | 30 | 5.4 | even | 2 | |||
25.33.c.b.18.15 | 30 | 5.2 | odd | 4 |